Critical point theory and its applications

Critical Point Theory and Its Applications

Volumn , Issue , 2006, Pages 1-318

  Zou, Wenming ^a   Schechter, Martin ^b  

^a TSINGHUA UNIVERSITY   (China)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84891410069     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1007/0-387-32968-4     Document Type: Book

References (396)

1. A. Abbondandolo, A new cohomology for the Morse theory of strongly indefinite functionals on Hilbert spaces, Topol. Meth. Nonl. Anal., 9(1997), 325-382.
2. A. Abbondandolo, Morse theory for Hamiltonian systems. Chapman & Hall/CRC Research Notes in Math., 425, Boca Raton, FL 2001.
3. A. Abbondandolo, J. Molina, Index estimates for strongly indefinite functionals, periodic orbits and homoclinic solutions of first order Hamiltonian systems, Calc. Var., 11(2000), 395-430.
4. R. A. Adams, Sobolev Space, Academic Press, New York-San Franciso-London, 1975.
5. S. Alama and Y.Y. Li, Existence of solutions for semilinear elliptic equations with indefinite linear part, J. Diff. Equations, 96(1992), 89-115.
6. S. Alama and Y.Y. Li, On "multibump" bound states for certain semilinear elliptic equations, Indiana J. Math., 41 (1992), 983-1026.
7. H. Amann, Ljusternik-Schnirelman theory and nonlinear eigenvalue problems. Math. Ann., 199(1972), 55-72.
8. H. Amann, Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces, SIAM, Review, 18(1976), 620-709.
9. H. Amann and E. Zehnder, Nontrivial solutions for a class of nonresonance problems and applications to nonlinear differential equations, Ann. Scuola Norm. Sup. Pisa, 7(1980), 539-603.
10. H. Amann and E. Zehnder, Periodic solutions of asymptotically linear Hamiltonian systems, Manuscr. Math., 32(1980), 149-189.
11. A. Ambrosetti, J. Azorero and I. Peral, Multiplicity results for some nonlinear elliptic equations, J. Funct. Anal, 137(1996), 219-242.
12. A. Ambrosetti and M. Badiale, Homoclinics: Poincare-Melnikov type results via variational approach, Ann. Inst. H. Poincare. Anal. Non Lineaire 15(1998), 233-252.
13. A. Ambrosetti and M. Badiale, Variational perturbative methods and bifurcation of bound states from the essential spectrum, Proc. Roy. Soc. Edinburgh Sect. A, 128(1998), 1131-1161.
14. A. Ambrosetti and M. L. Bertotti, Homoclinic for second order conservative systems. In: Partial diff. eqns. and related subjects (Trento, 1990), 21-37. Longman Sci. Tech., Harlow, 1992.
15. A. Ambrosetti, H. Brezis and G. Cerami, Combined effects of concave and convex nonlinearities in some elliptic problems, J. Funct. Anal., 122(1994), 519-543.
16. A. Ambrosetti and V. Coti Zelati, Multiplicite des orbites homoclines pour des systemes conservatifs, C.R. Acad. Sci. Paris, 314(1992), 601-604.
17. A. Ambrosetti, J. Garcia Azorero and I. P. Alonso, Multiplicity results for some nonlinear elliptic equations, J. Funct. Anal., 137(1996), 219-242.
18. A. Ambrosetti and G. Prodi, On the inversion of some differentiable mappings with singularities between Banach spaces, Ann. Mat. Pura Appl., 93(1972), 231-246.
19. A. Ambrosotti and P. H. Rabinowitz, Dual variational methods in critical point theory and applications, J. Funct. Anal, 14(1973), 349-381.
20. S. Angenent and R. van der Vorst, A superquadratic indefinite elliptic system and its Morse-Conley-Floer homology. Math. Z., 231(1999), 203-248.
21. G. Arioli, A note on quasilinear elliptic eigenvalues problems, E. J. Diff. Eqns., 47(1999), 1-12.
22. G. Arioli and A. Szulkin, Homoclinic solutions of Hamiltonian systems with symmmetry, J. Diff. Eqns., 158(1999), 291-313.
23. J. G. Azorero and I. P. Alonso, Multiplicity of solutions for elliptic problems with critical exponents or with a nonsymmetric term. Trans. Amer. Math. Soc, 323(1991), 887-895.
24. A. Bahri, Topological results on a certain class of functional and applications, J. Funct. Anal, 41(1981), 397-427.
25. A. Bahri and H. Berestycki, A perturbation method in critical point theory and applications, Trans. Amer. Math. Soc, 267(1981), 1-32.
26. A. Bahri and H. Berestycki, Forced vibrations of superquadratic Hamiltonian systems. Acta Math., 152(1984), 143-197.
27. A. Bahri and P. L. Lions, Remarks on the variational theory of critical points and applications, C. R. Acad. Sci. Paris Ser. I. Math., 301(1985), 145-148.
28. P. Bartolo, V. Benci and D. Fortunato, Abstract critical point theorems and applications to some nonlinear problems with strong resonance at infinity, Nonl. Anal. TMA, 7(1983), 981-1012.
29. T. Bartsch, Critical point theory on partially ordered Hilbert spaces, J. Funct. Anal, 186(2001), 117-152.
30. T. Bartsch, Infinitely many solutions of a symmetric Dirichlet problem. Nonlinear Analysis, TMA, 20(1993), 1205-1216.
31. T. Bartsch, K. C. Chang and Z. Q. Wang, On the Morse indices of signchanging solutions for nonlinear elliptic problems. Math. Z., 233(2000), 655-677.
32. T. Bartsch and M. Clapp, Critical point theory for indefinite functionals with symmetries, J. Funct. Anal, 138(1996), 107-136.
33. T. Bartsch and D. G. de Figueiredo, Infinitely many solutions of nonlinear elliptic systems. Topics in Nonl. Anal, 51-67, Progr. Nonl. Diff. Eqns. Appl, 35, Birkhauser, Basel, 1999.
34. T. Bartsch and Y. Ding, On a nonlinear Schrodinger equation with periodic potential. Math. Ann., 313 (1999), 15-37.
35. T. Bartsch and Y. Ding, Homoclinic solutions of an infinite-dimensional Hamiltonian systems. Math. Z., 240(2001), 289-310.
36. T. Bartsch and Y. Ding, Critical point theory with applications to asymptotically linear wave and beam equations, Nonl. Anal. TMA, 44(2001), 727-748.
37. T. Bartsch and S. Li, Critical point theory for asymptotically quadratic functionals and applications to problems with resonance, Nonl. Anal. TMA, 28(1997), 419-441.
38. T. Bartsch, Z. Liu and T. Weth, Sign changing solutions of superlinear Schrodinger equations, Comm. in Partial Differential Equations, 29 (2004), 25-42.
39. T. Bartsch, A. Pankov and Z. Q. Wang, Nonlinear Schrodinger equations with steep potential well, Comm. Contemp. Math., 4(2001), 549-569.
40. T. Bartsch and A. Szulkin, Hamiltonian systems: periodic and homoclinic solutions by variational methods. Handbook of Differential Equations-Ordinary Differential Equations, 2, Chapter 2, 77-146, (A. Canada, P. Drabek, A. Fonda, Eds.) Elsevier 2005.
41. T. Bartsch and Z. Q. Wang, Existence and multiple results for some superlinear elliptic problems on R, Comm. in Partial Diff. Eqns., 20(1995), 1725-1741.
42. T. Bartsch and Z. Q. Wang, On the existence of sign-changing solutions for semilinear Dirichlet problems, Topo. Meth. Nonl. Anal, 7(1996), 115-131.
43. T. Bartsch and Z. Q. Wang, Periodic solutions of spatially periodic, even Hamiltonian systems, J. Diff. Eqns., 135(1997), 103-128.
44. T. Bartsch and Z. Q. Wang, Sign changing solutions of nonlinear Schrodinger equations, Topo. Meth. Nonl. Anal, 13(1999), 191-198.
45. T. Bartsch, Z. Q. Wang and M. Willem, The Dirichlet problem for superlinear elliptic equations. Handbook of Differential Equations -Stationary Partial Differential equations, 2, Chapter 1, 1-55, (M. Chipot, P. Quittner, Eds.) Elsevier 2005.
46. T. Bartsch and T. Weth, A note on additional properties of sign changing solutions to superlinear elliptic equations, Topol. Methods in Nonl. Anal, 22(2003), 1-14.
47. T. Bartsch and T. Weth, Three nodal solutions of singularly perturbed elliptic equations on domains without topology, Ann. Inst. H. Poincare-Analyse Nonlin., 22 (2005), 259-281.
48. T. Bartsch and M. Willem, On an elliptic equation with concave and convex nonlinearities, Proc. Amer. Math. Soc, 123(1995), 3555-3561.
49. T. Bartsch and M. Willem, Periodic solutions of non-autonomous Hamiltonian systems with symmetries, J. reine angew. Math., 451(1994), 149-159.
50. T. Bartsch and M. Willem, Infinitely many nonradial solutions of a Euclidean scalar field equation, J. Funct. Aanl., 117(1993), 447-460.
51. V. Benci, On critical point theory for indefinite functionals in the presence of symmetries. Trans. Amer. Math. Soc, 274(1982), 533-572.
52. V. Benci, Introduction to Morse theory: A new approach. M. Matzen, A. Vignoh (eds). Topological Nonlinear Analysis, pp. 37-177. Birkhauser, Boston 1995.
53. V. Benci and G. Cerami, Existence of positive solutions of the equation N - 2 -Au + a{x)u = u in Rn, J. Funct Anal, 88 (1990), 90-117.
54. V. Benci and F. Giannoni, Homoclinic orbits on compact manifolds, J. Math. Anal Appl., 157(1991), 568-576.
55. V. Benci and P. H. Rabinowitz, Critical point theorems for indefinite functional. Invent Math., 52(1979), 241-273.
56. A. K. Ben-Naoum, C. Troestler and M. Willem, Extrema problems with critical Sobolev exponents on unbounded domains. Nonlinear Analysis TMA, 26(1995), 823-833.
57. H. Berestycki and D. G. de Figueiredo, Double resonance in semilinear elliptic problems, Comm. in Partial Differential Equations, 6 (1981), 91-120.
58. H. Berestycki and P. L. Lions, Nonlinear scalar field equations. I. Existence of a ground state. Arch. Rational Mech. Anal, 82(1983), 313-345.
59. P. Bolle, On the Bolza problem, J. Differential equations, 152(1999), 274-288.
60. J. F. Bonder, J. P. Pinasco and J. D. Rossi, Existence results for Hamiltonian elliptic systems with nonlinear boundary conditions, E. J. Diff. Eqns., 1999(1999), No. 40, 1-15.
61. J. F. Bonder and J. D. Rossi, Existence for an elliptic system with nonlinear boundary conditions via fixed point methods. Adv. Diff. Eqns., 6(2001), 1-20.
62. L. Boccardo and D. G. de Figueiredo, Some remarks on a system of quasilinear elliptic equations, NoDEA, 9(2002), 309-323.
63. R. Bott, Lectures on Morse theory, old and new. Bull. Amer. Math. Soc, 7(1982), 331-358.
64. H. Brezis, Analyse fonctionnelle, Masson, Paris, 1983.
65. H. Brezis, On a characterization of fiow invariant sets, Comm. Pure. Appl. Math., 23(1970), 261-263.
66. H. Brezis and T. Kato, Remarks on the Schrodinger operator with singular complex potentials, J. Math. Pures Appl, 58(1979), 137-151.
67. H. Brezis and E. Lieb, A relation between pointwise convergence of functions and convergence of functionals, Proc. Amer. Math. Soc, 88(1983), 486-490.
68. H. Brezis and L. Nirenberg, Forced vibrations for a nonlinear wave equation, Comm. Pure and Applied Math., 31(1978), 1-30.
69. H. Brezis, J. M. Coron and L. Nirenberg, Free vibrations for a nonlinear wave equation and a theorem of P. Rabinowitz, Comm. Pure and Applied Math., 33(1980), 667-689.
70. H. Brezis and L. Nirenberg, Remarks on Finding Critical Points, Comm. Pure and Applied Math., XLIV(1991), 939-963.
71. H. Brezis and L. Nirenberg, Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents, Comm. Pure Appl. Math., 36 (1983), 437-477.
72. H. Brezis and L. Nirenberg, Characterization of the ranges of some nonlinear operators and applications to boundary value problems, Ann. Acoula Norm. Sup. Pisa CL. Sci., 5(1978), 225-326.
73. B. Buffoni and L. Jeanjean, Minimax characterisation of solutions for a semi-linear elliptic equation with lack of compactness, Ann. Inst. H. Poincare-Analyse Nonlin., 10(1993), 377-404.
74. B. Buffoni, L. Jeanjean and C.A. Stuart, Existence of nontrivial solutions to a strongly indefinite semilinear equation, Proc. Amer. Math. Soc, 119 (1993), 179-186.
75. N. P. Cac, On nontrivial solutions of a Dirichlet problem whose jumping nonlinearity crosses a multiple eigenvalue, J. Diff. Eqns., 80(1989), 379-404.
76. P. Caldiroli and L. Jeanjean, Homoclinic and Heteroclinics for a class of conservative singular Hamiltonian systems, J. Diff. Eqns., 136(1997), 76-114.
77. L. Caklovic, S. Li and W. Willem, A note on Palais-Smale condition and coercivity, Diff. Int. Eqn., 3(1990), 799-800.
78. D. Cao, S. Peng, A global compactness result for singular elliptic problems involving critical Sobolev exponent, Proc. Amer. Math. Soc, 131(2003), 1857-1866.
79. P.C. Carriao and O.H. Miyagaki, Existence of homoclinic solutions for a class of time-dependent Hamiltonian systems, J. Math. Anal. Appl, 230(1999), 157-172.
80. S. Carl and K Perera, Sign-changing and multiple solutions for the p-Laplacian, Abstr. Appl. Anal, 7(2002), 613-625.
81. A. Castro, Reduction methods via minimax. Lecture Notes in Math., 957(1982), 1-20.
82. A. Castro and J. Cossio, Multiple solutions for a nonlinear Dirichlet problem, SIAM J. Math. Anal, 25(1994), 1554-1561.
83. A. Castro, J. Cossio and J. M. Neuberger, A sign changing solution for a superlinear Dirichlet problem. Rocky Mount. J. Math., 27(1997), 1041-1053.
84. A. Castro, J. Cossio and J. M. Neuberger, A minimax principle, index of the critical point, and existence of sign-changing solutions to elliptic BVPs, E. J. Diff. Eqns., 2(1999), 18pp.
85. A. Castro and M. Finan, Existence of many sign-changing nonradial solutions for semilinear elliptic problems on thin annuli, Topo. Meth. Nonlinear Anal, 13 (1999), 273-279.
86. G. Cerami, Un criterio di esistenza per i punti critici su varieta illimitate. Rend. Acad. Sci. Let. 1st. Lomhardo, 112(1978), 332-336.
87. G. Cerami, S. Solimini and M. Struwe, Some existence results for superlinear elliptic boundary value problems involving critical exponents, J. Funct. Anal, 69 (1986), 289-306.
88. J. Chabrowski and A. Szulkin, On a semilinear Schrodinger equation with critical Sobolev exponent, Proc. Amer. Math. Soc, 130(2002), 85-93.
89. J. Chabrowski, Weak convergence methods for semilinear elliptic equations. World Scientific Publishing Co., Inc., River Edge, NJ, 1999.
90. J. Chabrowski and J. Yang, On Schrodinger equation with periodic potential and critical Sobolev exponent, Topol Meth. Nonl Anal, 12 (1998), 245-261.
91. J. Chabrowski and J. Yang, Existence theorems for the Schrodinger equation involving a critical Sobolev exponent, Z. Angew. Math. Phys., 49(1998), 276-293.
92. F. C. Chang and L. Sanchez, Nontrivial periodic solutions of a nonlinear beam equation. Math. Meth. Appl Sci., (1982), 194-205.
93. K. C. Chang, A variant of the mountain pass lemma, Scientia Sinica, 26(1983), 1241-1255.
94. K. C. Chang, Infinite dimensional Morse theory and its apphcations, Presses Univ. Montreal, 1985.
95. K. C. Chang, On the homology method in the critical point theory. Pitman Research Notes in Mathematics Series, 269(1992), 59-77.
96. K. C. Chang, Infinite-dimensional Morse theory and multiple solution problems, Birkhduser, Boston, 1993.
97. K. C. Chang and N. Ghoussoub, The Conley index and the critical groups via an extension of Gromoll-Meyer theory, TMNA, 7(1996), 77-93.
98. K. C. Chang and M. Y. Jiang, Dirichlet problem with indefinite nonlinearities, Calc, Var., 20(2004), 257-282.
99. K. C. Chang, J. Liu and M. Liu, Nontrivial periodic solutions for strong resonance Hamiltonian systems, Ann. Inst. H. Poincare-Analyse Nonlin., 14(1997), 103-117.
100. G. Chen, W. Ni and J. Zhou, Algorithms and visualization for solutions of nonlinear elliptic equations, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10(2000), 1565-1612.
101. C. Christine and N. Ghoussoub, Deformation from symmetry and multiplicity of solutions in non-homogeneous problems. Discrete and Continuous Dynamical Systems, 8(2002), 267-281.
102. D. C. Clark, A variant of the Ljusternik-Schnirelman theory, Indiana Univ. Math. J., 22(1972), 65-74.
103. P. Clement, P. Felmer and E. Mitidieir, Homoclinic orbits for a class of infinite dimensional Hamiltonian systems, Ann. Acoula Norm. Sup. Pisa CL. Sci., 24(1997), 367-393.
104. Ph. Clement, D. G. de Figueiredo and E. Mitidieri, Positive solutions of semilinear elliptic systems, Comm. Part. Diff. Eqns., 17(1992), 923-940.
105. C. C. Conley and E. Zehnder, Morse type index theory for fiows and periodic solutions for Hamiltonian equations, Comm. Pure Appl. Math., 37(1984), 207-253.
106. D. G. Costa, On a class of elliptic systems in Rn, Electronic J. Diff. Eqns., 7(1994), 1-14.
107. D. G. Costa, A note on unbounded perturbations of linear resonant problems, Trab. de Math. no 245, Univ. de Brasiilia, 1989.
108. D. Costa, Z. Ding and J. Neuberger, A numerical investigation of signchanging solutions to superlinear elliptic equations on symmetric domains, J. Comput. Appl. Math., 131(2001), 299-319.
109. D. G. Costa and C. A. Magalhaes, Variational elliptic problems which are nonquadratic at infinity. Nonlinear Analysis TMA, 23(1994), 1401-1412.
110. D. G. Costa and C. A. Magalhaes, A variational approach to subquadratic perturbations of elliptic systems, J. Diff. Eqns., 111(1994), 103-122.
111. D. G. Costa and C. A. Magalhaes, Variational elliptic problems which are nonquadratic at infinity, Nonl Anal. TMA, 23(1994), 1401-1412.
112. D. G. Costa and C. A. Magalhaes, A variational approach to noncooperative elliptic systems, Nonl. Anal. TMA, 25(1995), 699-715.
113. D. G. Costa and C. A. Magalhaes, A unified approach to a class of strongly indefinite functional, J. Diff. Eqns., 122(1996), 521-547.
114. D. G. Costa and E. A. B. Silva, The Palais-Smale condition versus coercivity, Nonl. Anal. TMA, 16(1991), 371-381.
115. D. G. Costa and E. A. B. Silva, A note on problems involving critical Sobolev exponents, Diff. Int. Eqns., 8(1995), 673-679.
116. V. Coti Zelati, I. Ekeland and E. Sere, A variational approach to homoclinic orbits in Hamiltonian systems. Math. Ann., 228(1990), 133-160.
117. V. Coti Zelati and P. H. Rabinowitz, Homoclinic orbits for second order Hamiltonian systems possessing superquadratic potentials, J. Amer. Math. Soc, 4 (1991), 693-727.
118. V. Coti-Zelati and P. H. Rabinowitz, Homoclinic type solutions for a semilinear elliptic PDE on Rn, Comm. Pure Appl. Math., 45(1992), 1217-1269.
119. M. Cuesta, D. G. de Figueiredo and J. P. Gossez, The beginning of the Fucik spectrum for the p-Laplacian, J. Diff. Eqns., 159(1999), 212-238.
120. E. N. Dancer, On the Dirichlet problem for weakly nonlinear elliptic partial differential equations, Proc. Royal Soc. Edinburgh, 76A(1977), 283-300.
121. E. N. Dancer, Degenerate critical points, homotopy indices and Morse inequalities, J. Reine Angew. Math., 350(1984), 1-22.
122. E. N. Dancer, Multiple solutions of asymptotically homogeneous problems, Ann Math Pura Appl., 152(1988), 63-78.
123. E. N. Dancer, Remarks on jumping nonlinear it ies. Topics in Nonlinear Analysis, Escher and Simonett, eds.), Birkhauser, Basel, 1999, 101-115.
124. E. N. Dancer, Some results for jumping nonlinearities, Toplogical Methods in Nonlinear Analysis, 19(2002), 221-235.
125. E. N. Dancer and K. Perera, Some remarks on the Fucik spectrum of the p-Laplacian and critical groups, J. Math. Anal. Appl., 254(2001), 164-177.
126. E. N. Dancer and Y. Du, On sign-changing solutions of certain semilinear elliptic problems, Appl. Anal, 56(1995), 193-206.
127. E. N. Dancer and S. Yan, On the profile of the changing sign mountain pass solutions for an elliptic problem. Trans. Amer. Math. Soc, 364 (2002), 3573-3600.
128. E. N. Dancer and Z. Zhang, Fucik spectrum, sign-changing and multiple solutions for semilinear elliptic boundary value problems with resonance at infinity, J. Math. Anal. Appl, 250(2000), 449-464.
129. M. Degiovanni and L. Olian Fannio, Multiple periodic solutions of asymptotically linear Hamiltonian systems, Nonl. Anal. TMA, 26(1996), 1437-1446.
130. K. Deimling, Ordinary differential equations in Banach spaces. Lecture Notes in Mathematics, Vol. 596. Springer-Verlag, Berlin-New York, 1977.
131. K. Deimling, Nonlinear Functional Analysis, Springer-Verlag, 1985.
132. Y. Ding, Existence and multiciplicity results for homoclinic solutions to a class of Hamiltonian systems, Nonl. Anal. TMA, 25 (1995), 1095-1113.
133. Y. Ding and M. Girardi, Periodic and homoclinic solutions to a class of hamiltonian systems with the potentials changing sign, Dyn. Sys. Appl., 2 (1993), 131-145.
134. Y. Ding and S. Li, Homoclinic orbits for first order Hamiltonian systems, J. Math. Anal. Appl, 189 (1995), 585-601.
135. Y. Ding and S. Luan, Multiple solutions for a class of nonlinear Schrodinger equations, J. Diff. Eqns., 207(2004), 423-457.
136. Y. Ding and M. Willem, Homoclinic orbits of a Hamiltonian system, Z. Angew. Math. Phys., 50 (1999), 759-778.
137. Z. Ding, D. Costa and G. Chen, A high-linking algorithm for signchanging solutions of semilinear elliptic equations. Nonlinear Analysis, 38(1999), 151-172.
138. A. Dold, Lectures on Algebraic Topology, Springer-Verlag, Berlin, 1972.
139. G. C. Dong and S. Li, On the existence of infinitely many solutions of the Dirichlet problem for some nonlinear elliptic equations, Sci. Sinica Ser. A 5(1982), 468-475.
140. D. Dong and Y. Long, The iteration formula of the Maslov-type index theory with applications to nonlinear Hamiltonian systems. Trans. AMS, 349(1997), 2619-2661.
141. P. Drabek, Solvability and bifurcation of nonlinear equations. Pitman research notes in mathematics series, 264. Longman Sci. & Tech., Harlow.
142. P. Drabek and S. Robinson, Resonance problems for the p-Laplacian, J. Funct. Anal., 169(1999), 189-200.
143. Y. Du, A deformation lemma and some critical point theorems. Bull. Austral. Math. Soc, 43(1991), 161-168.
144. N. Dunford and J. T. Schwartz, Linear Operators, Part I, Interscience, 1967.
145. I. Ekeland, On the variational principle, J. Math. Anal. Appl., 47(1974), 324-353.
146. I. Ekeland and N. Ghoussoub, Selected new aspects of the calculus of variations in the large. Bull. Amer. Math. Soc. (N.S.), 39(2002), 207-265.
147. L. C. Evans, Partial Differential Equations, Graduate Studies in Math. Vol. 19, Amer. Math. Soc, 1998.
148. G. Fei, Maslov-type index and periodic solution of asymptotically linear Hamiltonian systems which are resonant at infinity, J. Diff. Eqn., 121(1995), 121-133.
149. G. Fei, Nontrivial periodic solutions of asymptotically linear Hamiltonian systems, E. J. Diff. Eqns., 69(2001), 1-17.
150. G. Fei and Q. Qiu, Periodic solutions of asymptotically linear Hamiltonian systems, Chinese Ann. Math. Ser. B, 18(1997), 359-372.
151. G. Feireisl, Time periodic solutions to a semilinear Beam equation, Nonl. Anal. TMA, 12(1988), 279-290.
152. P. Felmer, Periodic solutions of superquadratic Hamiltonian systems, J. Diff. Eqns., 102(1993), 188-207.
153. P. Felmer, Heteroclinic orbits for spatially periodic Hamiltonian systems, Ann. Inst. H. Poincare Anal. Non Lineaire, 8(1991), 477-497.
154. P. Felmer, R. F. Manasevich and F. de Thelin, Existence and uniqueness of positive solutions for certain quasilinear elliptic systems, Comm. Par. Diff. Eqns., 17(1992), 2013-2029.
155. A. Ferrero and F. Gazzola, Existence of solutions for singular critical growth semilinear elliptic equations, J. Diff. Eqns., 177(2001), 494-522.
156. D. G. de Figueiredo, Nonlinear elliptic systems. An. Acad. Bras. Ci., 72(2000), 453-469.
157. D. G. de Figueiredo, Positive solutions of semilinear elliptic equations. Springer Lecture Notes in Mathematics, 957(1982), 34-87.
158. D. G. de Figueiredo, Semilinear elliptic systems: a survey of superlinear problems, Resenhas IME-USP, 2(1996), 373-391.
159. D. G. de Figueiredo and P. L. Felmer, On superquadratic elliptic systems. Trans. Amer. Math. Soc, 343(1994), 99-116.
160. D. G. de Figueiredo and C. A. Magalhaes, On nonquadratic Hamiltonian elliptic systems. Adv. Diff. Eqns., 1 (1996), 881-898.
161. D. G. de Figueiredo and I. Massabo, Semilinear elliptic equations with the primitive of the nonlinearity interacting with the first eigenvalue, J. Math. Anal. Appl., 156(1991), 381-394.
162. D. G. de Figueiredo and E. Mitidieri, A maximum principle for an elliptic system and applications to semilinear problem, SIAM J. Math. Anal, 17(1986), 836-849.
163. D. G. de Figueiredo and P. L. Lions, On pairs of positive solutions for a class of semilinear elliptic problems, Indiana Univ. Math. J., 34(1985), 591-606.
164. D. G. de Figueiredo and J. Yang, Decay, symmmetry and existence of positive solutions of semilinear elliptic systems, Nonl Anal, TMA, 33(1998), 211-234.
165. M. F. Furtado, L. A. Maia and E. A. B. Silva, On a double resonant problem in Rn, Differential Integral Equations, 15(2002), 1335-1344.
166. M. F. Furtado, L. A. Maia and E. A. B. Silva, Solutions for a resonant elliptic system with coupling in Rn, Comm. in Partial Differential Equations, 27 (2002), 1515-1536.
167. S. Fucik, Boundary value problems with jumping nonlinear it ies, Casopis Pest Mat, 101 (1976), 69-87.
168. T. Gallouet and O. Kavian, Resultats d'existence et de non existence pour certains problems demi lineaires a I'infini, Ann. Fac. Sci. Toulouse Math., 3(1981), 201-246.
169. J. P. Garcia Azorero and I. Peral Alonso, Hardy inequalities and some critical elliptic and parabolic problems, J. Differential Equations, 144(1998), 441-476.
170. N. Ghoussoub, Duality and perturbation methods in critical point theory, Cambridge University Press, 1993.
171. N. Ghoussoub, A min-max principle with a relaxed boundary condition, Proc. Amer. Math, Soc., 117(1993), 439-447.
172. N. Ghoussoub and C. Yuan, Multiple solutions for quasi-linear PDEs involving the critical Sobolev and Hardy exponents. Trans. Amer. Math. Soc, 352(2000), 5703-5743.
173. F. Giannoni, L. Jeanjean and K. Tanaka, Homoclinic orbits on noncompact Riemannian manifolds for second order Hamiltonian systems. Rend. Sem. Mat Univ. Padova, 3(1995), 153-176.
174. D. Gilbarg and N.S. Trudinger, Elliptic partial differential equations of second order. Springer 2001.
175. D. Gromoll and W. Meyer, On differentiable functions with isolated critical points. Topology, 8(1969), 361-369.
176. M. R. Grossinho and S. A. Tersian, An introduction to minimax theorems and their applications to differential equations, Nonconvex optimization and its applications. Vol. 52, Kluwer Academic Publishers, 2001.
177. D. Guo, Nonlinear functional analysis, San Dong Sci. Tech. Press, 1985 (in Chinese).
178. Y. Guo, Nontrivial periodic solutions for asymptotically linear Hamiltonian systems with resonance, J. Diff. Eqns., 175(2001), 71-87.
179. H. P. Heinz, Free Ljusternik-Schnirelman theory and the bifurcation diagrams of certain singular nonlinear systems, J. Diff. Eqns., 1987, 263-300.
180. H. P. Heinz, Bifurcation from the essential spectrum for nonlinear perturbations of Hill's equation, in 'Differential Equations-Stability and Contror(ed. S. Elaydi), Marcel Dekker, New York, (1990), 219-226.
181. H. P. Heinz, Lacunary bifurcation for operator equations and nonlinear boundary value problems on Rn, Proc. Royal Soc. Edinburgh, 118(1991), 237-270.
182. H. P. Heinz, T. Küpper and C. A. Stuart, Existence and bifurcation of solutions for nonlinear perturbation of the periodic Schrodinger equation, J. Diff. Eqns., 100(1992), 341-354.
183. H. P. Heinz and C. A. Stuart, Solvability of nonlinear equations in spectral gap of the linearisation, Nonl. Anal. TMA, 19(1992), 145-165.
184. N. Hirano, Existence of infinitely many solutions for sublinear ellitic problems, J. Math. Anal. Appl., 278(2003), 83-92.
185. N. Hirano, S. Li and Z. Q. Wang, Morse theory without (PS) condition at isolated value and strong resonance problems, Cal. Var., 10(2000), 223-247.
186. N. Hirano and T. Nishimura, Multiplicity results for semilinear elliptic problems at resonance and with jumping nonlinearities, J. Math. Anal. Appl., 180(1993), 566-586.
187. H. Hofer, On strongly indefinite functional with applications. Trans. Amer. Math. Soc, 275(1983), 185-214.
188. H. Hofer and K. Wysocki, First order elliptic systems and the existence of homoclinic orbits in Hamiltonian systems. Math. Ann., 228 (1990), 483-503.
189. J. Hulshof and R. van der Vorst, Differential systems with strongly indefinite variational structure, J. Funct. Anal., 114(1993), 32-58.
190. M. Izydorek, Equivariant Conley index in Hilbert spaces and applications to strongly indefinite problems, Nonl Anal TMA, 51(2002), 33-66.
191. L. Jeanjean, On the existence of bounded Palais-Smale sequences and applications to a Landesman-Lazer type problem, Proc. Roy. Soc. Edinburgh A, 129 (1999), 787-809.
192. L. Jeanjean, Solutions in spectral gaps for a nonlinear equation of Schrodinger type, J. Diff. Equations, 112 (1994), 53-80.
193. L. Jeanjean, Local conditions insuring bifurcation from the continuous spectrum. Math. Z., 232(1999), 651-664.
194. L. Jeanjean, Variational methods and applications to some nonlinear problems. Memoir for Hahilitation of Louis Jeanjean, 1999, (Private Communication).
195. L. Jeanjean and K. Tanaka, A positive solution for an asymptotically linear elliptic problems on Rn autonomous at infinity, ESAIM Control Optim. Calc. Var., 7(2002), 597-614.
196. L. Jeanjean and J. F. Toland, Bounded Palais-Smale Mountain-Pass sequence, C. R. Acad. Sci. Paris, 327(1998), 23-28.
197. M. Jiang, Periodic solutions of second order superquadratic Hamiltonian systems with potential changing sing (I, II), J. Diff. Eqns., (to appear).
198. T. Kato, Perturbation theory for linear operators. Springer-Verlag, Berlin, 1980.
199. P. Krejci, On solvability of equations of the 4th order with jumping nonlinear it ies, Cas. pest, met., 108(1983), 29-39.
200. W. Kryszewski and A. Szulkin, An infinite dimensional Morse theory with applications. Trans. Amer. Math. Soc, 349(1997), 3181-3234.
201. W. Kryszewski and A. Szulkin, Generalized linking theorem with an application to a semilinear Schrodinger equation. Adv. Diff. Eqns., 3 (1998), 441-472.
202. P. Kuchment, Floquet Theory for Partial Differential Equations, Birkhduser, Basel, 1993.
203. A. C. Lazer, Introduction to multiplicity theory for boundary value problems with asymmetric nonlinearities. Partial Diff. Eqns., F. Cardos at al, Eds., Lecture Notes in Math., 1324(1988), Springer N. Y., 137-165.
204. A. C. Lazer and P. J. Mckenna, Critical point theory and boundary value problems with nonlinearities crossing multiple eigenvalues, I Comm. in Partial Diff. Equns., 10 (1985), 107-150
205. A. C. Lazer and P. J. Mckenna, Critical point theory and boundary value problems with nonlinearities crossing multiple eigenvalues, II Comm. Partial Diff. Equns., 11 (1986), 1653-1676.
206. A. C. Lazer and P. J. Mckenna, Large amplitude periodic oscillations in suspension bridges: Some new connections with nonlinear analysis, SIAM Rev., 32(1990), 537-578.
207. A. C. Lazer and P. J. Mckenna, Nonlinear flexings in a periodically forced floating beam. Math. Methods Appl. Sci., 14(1991), 1-33.
208. A. C. Lazer and S. Solimini, Nontrivial solutions of operator equations and Morse indices of critical points of min-max type, Nonl. Anal. TMA, 12(1988), 761-775.
209. G. Li and A. Szulkin, An asymptotically periodic Schrodinger equation with indeflnite linear part, Commun. Contemp. Math., 4(2002), 763-776.
210. P. Li and S. T. Yau, On the Schrodinger equation and the eigenvalue problem, Comm. Math. Phys., 88(1983), 309-318.
211. S. Li, Some existence theorems of critical points and applications, IC/86/90 Report, ICTP, Italy.
212. S. Li and J. Liu, Computation of critical groups at degenerate critical point and applications to nonlinear differential equations with resonance, Houston J. Math., 25(1999), 563-582.
213. S. Li and J. Liu, Morse theory and asymptotic linear Hamiltonian systems, J. Diff. Eqns., 78(1989), 53-73.
214. S. Li, K. Perera and J. Su, On the role played by the Fucik spectrum in the determination of critical groups in elliptic problems where the asymptotic limits may not exist, Nonl. Anal. TMA, 49(2002), 603-611.
215. S. Li and A. Szulkin, Periodic solutions of an asymptotically linear wave equation, Topol. Meth. Nonl. Anal, 1(1993), 211-230.
216. S. Li and A. Szulkin, Periodic solutions for a class of nonautonomous Hamiltonian systems, J. Diff. Eqns., 112 (1994), 226-238.
217. S. Li and Z. Q. Wang, Ljusternik-Schnirelman theory in partially ordered Hilbert spaces, Tran. Amer. Math. Soc, 354 (2002), 3207-3227.
218. S. Li and Z. Q. Wang, Mountain Pass theorem in order intervals and multiple solutions for semilinear elliptic Dirichlet problems, J. d' Analyse Math., 81(2000), 373-396.
219. S. Li and M. Willem, Applications of local linking to critical point theory, J. Math. Anal. Appl, 189(1995), 6-32.
220. S. Li and W. Zou, The computations of the critical groups with an application to elliptic resonant problem at higher eigenvalue, J. Math. Anal. Appl, 235(1999), 237-257.
221. S. Li and W. Zou Remarks on a class of elliptic problems with critical Sobolev exponants, Nonlinear Analysis, TMA, 32(1998), 769-774.
222. Y. Li, On a nonlinear elliptic eigenvalue problem, J. Diff. Eqns., 117(1995), 151-164.
223. Y. Li, Three solutions of a semilinear elliptic eigenvalue problem. Acta Math. Sinica, 11(1995), 142-152.
224. Y. Y. Li, On -Ai = K{x)u in Rn, Comm. Pure Appl. Math., 46(1993), 303-340.
225. Y. Y. Li, Prescribing scalar curvature on Sn and related problems. Part I, J. Diff. Equations, 120(1995), 319-410.
226. J. L. Lions and E. Magenes, Problemes aux limites non homogenes et applications. Vol. I, Dunod, Paris, 1968.
227. P.L. Lions, On the existence of positive solutions of semilinear elliptic equations, SIAM Review, 24(1982), 441-467.
228. P L. Lions, The concentration-compactness principle in the calculus of variations. The locally compact case. Part II, Ann. Inst. H. Poincare, Analyse nonlineaire, 1(1984), 223-283.
229. C. Liu, Iteration theory of Maslov-type index and its applications, Proc. of the workshop on Morse theory, mimimax theory and their appl. to nonlinear diff. eqns., Morningside center of Math., Beijing, 1999. (Editors: H. Brezis, S. Li, J. Liu and P. Rabinowitz; Inter. Press), 125-137.
230. J. Liu, The Morse index of a saddle point. Systems Science and Mathematical Sciences, 2 (1989), 32-39.
231. J. Liu, Free vibrations for an asymmetric beam equation, Nonl. Anal. TMA, 51(2002), 487-497.
232. J. Liu, Free vibrations for an asymmetric beam equation, II, Nonl Anal TMA, 56(2004), 415-432.
233. J. Liu and S. Li, Some existence theorems on multiple critical points and their applications, Kexue Tonghao, 17(1984), 1025-1027.
234. J. Liu and S. Liu, The existence of multiple solutions to quasilinear elliptic equations. Bull. London Math. Soc, 37(2005), 592-600.
235. J. Liu and S. Wu, Calculating critical groups of solutions for elliptic problem with jumping nonlinearity, Nonl. Anal. TMA, 49(2002), 779-797.
236. Z. Liu, S. Li and Z. Q. Wang, Positive solutions of elliptic boundary value problems without the (PS) type assumption, Indiana Univ. Math. J., 50(2001), 1347-1369.
237. Z. Liu and Z. Wang, On the Ambrosetti-Rabinowitz superlinear condition. Adv. Nonl. Stud., 4(2004), 251-272.
238. N. G. Lloyd, Degree theory, Camh. Univ. Press, 1978.
239. Y. Long, Multiple solutions of perturbed superquadratic second order Hamiltonian systems. Trans. Amer. Math. Soc, 311(1989), 749-780.
240. Y. Long, Maslov-type index theory and asymptotically linear Hamiltonian systems. In Dyna. Syst. and Rel. Topics. Shiraiwa ed. World Sci. 1991, 333-341.
241. Y. Long, Maslov-type index, degenerate critical points, and asymptotically linear Hamiltonian systems. Science in China (Ser. A), 33(1990), 1409-1419.
242. Y. Long, Index theory for symplectic paths with applications, Birkhduser, Basel, 2002.
243. Y. Long and X. Xu, Periodic solutions for a class of nonautonomous Hamiltonian systems, Nonl. Anal. TMA, 41(2000), 455-463.
244. Y. Long and E. Zehnder, Morse theory for forced oscillations of asymptotically linear Hamiltonian systems. In "Stochastic process. Physics and geometry", Proc. of Conf. in Asconal/ Locarno, Switzerland, Edited by S. Albeverio and others. World Sci., 1990, 528-563.
245. W. Lu, Variational Methods in Differential Equations, Science Press, 2003 (in Chinese).
246. D. Lupo and A. M. Micheletti, Nontrivial periodic solutions for an asymptotically linear beam equation, Dynam. Syst. Appl., 4(1995), 147-155.
247. D. Lupo and A. M. Micheletti, Two applications of a three critical points theorem, J. Diff. Eqns., 132(1996), 222-238.
248. C. A. Magalhaes, Semilinear elliptic problem with crossing of multiple eigenvalues, Comm. Part Diff. Eqns., 15(1990), 1265-1292.
249. C. A. Magalhaes, Multiplicity results for a semilinear elliptic problems with crossing of multiple eigenvalues, Diff. Int. Eqns., 4(1991), 129-136.
250. C. A. Margulies and W. Margulies, An example of the Fucik spectrum, Nonl. Anal. TMA, 29(1997), 1373-1378.
251. A. Marino and C. Saccon, Some variational theorems of mixed type and elliptic problems with jumping nonlinearities, Ann. Scuola Norm. Sup. Pisa CI. Sci. (4), XXV(1997), 631-665.
252. J. Mawhin and M. Willem, Critical point theory and Hamiltonian systems. Springer-Verlag, New York, 1989.
253. A. M. Micheletti, A remark on the resonance set for a semilinear elliptic equation, Proc. Roy. Soc. Edinb. Sect, A 124(1994), 803-809.
254. A. M. Micheletti and A. A. Pistoia, A note on the resonance set for a semilinear elliptic equation and an application to jumping nonlinearities, Topol. Meth. Nonl. Anal, 6(1995), 67-80.
255. A. M. Micheletti and A. A. Pistoia, On the Fucik spectrum of the p-Laplacian, Diff. Int Eqns., 14(2001), 867-882.
256. A. M. Micheletti, A. A. Pistoia and C. Saccon, Nontrivial solutions for a floating beam equation, Ricerche Mat., 48 (1999), 187-197.
257. A. M. Micheletti and C. Saccon, Multiple nontrivial solutions for a floating beam equation via critical point theory, J. Diff. Eqns., 170(2001), 157-179.
258. J. Milnor, Morse Theory, Princeton Univ. Press, Princeton, 1963.
259. M. Morse, Relations between the critical points of a real funtion of n independent variables. Trans. Amer. Math. Soc, 27(1925), 345-396.
260. M. Nagumo, A theory of degree of mapping based on inflnitesimal analysis, Amer. J. Math., 73(1951), 485-496.
261. M. Nagumo, A note on the theory of degree of mapping in Euclidean space, Osaka Math. J., 4(1952), 1-5.
262. L. Nirenberg, On elliptic partial differential equations, Ann. Scuola Norm. Sup. Pisa., 13(1959), 115-162.
263. L. Nirenberg, Topics in Nonlinear Functional Analysis, Amer. Math. Soc. and Courant Institute of Math., 2001.
264. L. Nirenberg, Variational and topological methods in nonlinear problemss. Bull. Amer. Math, Soc., 4(1981), 267-302.
265. L. Nirenberg, Variational methods in nonliner problems. Topics in calculus of variations (Montecatini Terme, 1987), 100-119, Lecture Notes in Math., 1365, Springer, Berlin-New York, 1989.
266. J. M. Neuberger, A numerical method for finding sign-changing solutions of superlinear Dirichlet problems. Nonlinear World, 4(1997), 73-83.
267. J. Neuberger and J. W. Swift, Newton's method and Morse index for semilinear elliptic PDEs, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 11(2001), 801-820.
268. W. Omana and M. Willem, Homoclinic orbits for a class of Hamiltonian systems, Diff. Int. Eqns., 5 (1992), 1115-1120.
269. R. Palais, Morse theory on Hilbert manifolds. Topology, 2(1963), 299-340.
270. R. Palais, Ljusternik-Schnirelman theory on Banach manifolds. Topology, 5(1966), 115-132.
271. R. Palais, Homology theory of infinite dimensional manifolds. Topology, 5(1966), 1-16.
272. R. Palais and S. Smale, A generalized Morse theory. Bull. Amer. Math. Soc, 70(1964), 165-171.
273. A. A. Pankov and K. Pflüger, On a semilinear Schrodinger equation with periodic potential Nonl. Anal. 33(1998), 593-609.
274. E. Paturel, Multiple homoclinic orbits for a class of Hamiltonian systems, Calc. Var., 12(2001), 117-143.
275. K. Perera, Critical groups of pairs of critical points produced by linking subsets, J. Differential Equations, 140(1997), 142-160.
276. K. Perera, Multiplicity results for some elliptic problems with concave nonlinear it ies, J. Differential Equations, 140(1997), 133-141.
277. K. Perera, Critical groups of critical points produced by local linking with applications, Abstr. Appl. Anal., 3(1998), 437-446.
278. K. Perera, Homological local linking, Abstr. Appl. Anal, 3(1998), 181-189.
279. K. Perera, Applications of local linking to asymptotically linear elliptic problems at resonance, NoDEA, 6 (1999), 55-62.
280. K. Perera, p-Super linear problems with jumping nonlinear it ies. Nonlinear analysis and applications: to V. Lakshmikantham on his 80th birthday, Vol. 1-2, 823-829, Kluwer Acad. Publ, Dordrecht, 2003.
281. K. Perera, On the Fucik spectrum of the p-Laplacian, NoDEA, 11(2004), 259-270.
282. K. Perera and M. Schechter, Type (II) regions between curves of the Fucik spectrum and critical groups, Topol. Meths. in Nonl. Anal., 12(1999), 227-243.
283. K. Perera and M. Schechter, Double resonance problems with respect to the Fucik spectrum, Indiana Univ. Math. J., 52(2003), 1-17.
284. K. Perera and M. Schechter, The Fucik spectrum and critical groups, Proc. Amer. Math. Soc, 129(2001), 2301-2308.
285. K. Perera and M. Schechter, A generalization of the Amann-Zehnder theorem to nonresonance problems with jumping nonlinearities, NoDEA, 7(2000), 361-367.
286. K. Perera and M. Schechter, Double resonance problems with respect to the Fucik spectrum, Indiana Univ. Math. J., 52(2003), 1-17.
287. K. Perera and M. Schechter, Morse index estimates in saddle point theorems without a finite-dimensional closed loop, Indiana Univ. Math. J., 47, 1083-1095.
288. K. Perera and A. Szulkin, p-Laplacian problems where the nonlinearity crosses an eigenvalue. Discrete Contin. Dyn. Syst, 13(2005), 743-753.
289. L. Pisani, Existence of periodic solutions for Hamiltonian systems at resonance, NoDEA, 4(1997), 61-76.
290. P. Rabinowitz, Periodic solutions of Hamiltonian systems, Comm. Pure Appl. Math., 31(1978), 157-184.
291. P. Rabinowitz, Free vibrations for a semilinear wave equation, Comm. Pure Appl. Math., 31(1978), 31-68.
292. P. Rabinowitz, Periodic solutions of large norm of Hamiltonian systems, J. Diff. Eqns., 50(1983), 33-48.
293. P. Rabinowitz, Minimax methods in critical point theory with applications to differential equations, Conf. Board of Math. Sci. Reg. Conf. Ser. in Math., No. 65, Amer. Math. Soc., 1986.
294. P. Rabinowitz, Homoclinic orbits for a class of Hamiltonian systems, Proc. Roy. Soc. Edinburgh, 114 (1990), 33-38.
295. P. Rabinowitz, On a class of nonlinear Schrodinger equations, Z. Angew. Math. Phys., 43(1992), 270-291.
296. P. Rabinowitz, Multiple critical points of perturbed symmetric functional, Tran. Amer. Math. Soc, 272(1982), 753-769.
297. P. Rabinowitz and K. Tanaka, Some results on connecting orbits for a class of Hamiltonian systems. Math. Z., 206(1991), 472-499.
298. M. Ramos and C. Rebelo, A unified approach to min-max critical point theorems, Portugal. Math., 51(1994), 489-516.
299. M. Ramos and L. Sanchez, Homotopical linking and Morse index estimates in min-max theorem, manuscripta math., 87(1995), 269-284.
300. M. Ramos, S. Terracini and C. Troestler, Superlinear indefinite elliptic problems and Pohozaev type inentities, J. Funct. Anal, 159(1998), 596-628.
301. M. Reed and B. Simon, Methods of modern mathematical physics. Vol. IV, Academic Press, New York, 1978.
302. E. H. Rothe, Morse theory in Hilbert space. Rocky M. J. Math., 3(1973), 251-274.
303. B. Ruf, On nonlinear elliptic problems with jumping nonlinearites, Ann. Mat. Pura Appl, 128(1981), 133-151.
304. D. Ruiz and M. Willem, Elliptic problems with critical exponents and Hardy potentials, J. Diff. Eqns., 190(2003), 524-538.
305. A. Sard, The measure of critical values of differentiable maps. Bull. Amer. Math. Soc, 48(1942), 883-890.
306. M. Schechter, The Hampwile theorem for nonhnear eigenvalues, Duke Math. J., 59(1989), 325-335.
307. M. Schechter, The Fucik spectrum, Indiana Univ. Math. J., 43 (1994), 1139-1157.
308. M. Schechter, SuperUnear elhptic boundary value problems, Manuscripta Math., 86 (1995), 253-265.
309. M. Schechter, New linking theorem. Rend. Sem. Mat. Univ. Padova, 99(1998), 1-15.
310. M. Schechter, Linking methods in critical point theory, Birkhduser, Boston, 1999.
311. M. Schechter, Resonance problems with respect to the Fucik spectrum. Trans. Amer. Math. Soc, 352(2000), 4195-4205.
312. M. Schechter, Splitting subspaces and saddle points. Applicable Analysis, 49(1993), 33-48.
313. M. Schechter, Critical point theory with weak-to-weak linking, Comm. Pure Appl. Math., 51 (1998), 1247-1254.
314. M. Schechter, Some recent results in critical point theory. Pan American Mathematical Journal, 12(2002), 1-19.
315. M. Schechter, Type (II) regions between curves of the Fucik spectrum, NoDEA, 4(1997), 459-476.
316. M. Schechter, A bounded mountain pass lemma without the (PS) condition and applications. Trans. Amer. Math. Soc, 331(1992), 681-704.
317. M. Schechter, The intrinsic mountain pass. Pacific J. Math., 171(1995), 529-544.
318. M. Schechter, Eigenvalue problems for semilinear equations. Spectral and scattering theory (Newark, DE, 1997), 157-175, Plenum, New York, 1998.
319. M. Schechter, Critical points when there is no saddle point geometry, Topol. Methods Nonlinear Anal, 6(1995), 295-308.
320. M. Schechter, Infinite-Dimensional Linking, Duke Mathematical Journal, 94(1998), 573-595.
321. M. Schechter, The saddle point alternative, Amer. J. Math., 117(1995), 1603-1626.
322. M. Schechter and K. Tintarev, Pairs of critical points produced by linking subsets with applications to semilinear elliptic problems, Bull Soc. Math. Belg., 44(1994), 249-261.
323. M. Schechter and K. Tintarev, Critical points for pairs of functionals and semilinear elliptic equations, in Calculus of Variations, Applications and Computations (ed. C Bandle et al), Pitman Research Notes in Mathematics, No. 326(1995), 245-253.
324. M. Schechter and W. Zou, Double linking theorem and multiple solutions, J. Functional Analysis, 205(2003), 37-61.
325. M. Schechter and W. Zou, Homoclinic orbits for Schrodinger systems, Michigan Math. J., 51(2003), 59-71.
326. M. Schechter and W. Zou, On functionals bounded from below. Functional Analysis and its Application, 37(2003), 75-80.
327. M. Schechter and W. Zou, Weak linking, Nonl. Anal. TMA, 55(2003), 695-706.
328. M. Schechter and W. Zou, Weak linking theorems and schrodinger equations with critical Sobolev exponent. Control, Optimization and Calculus of Variations, 9(2003), 601-619.
329. M. Schechter and W. Zou, Superlinear problem. Pacific J. Math., 214(2004), 145-160.
330. M. Schecher and W. Zou, Infinite-dimensional linking theorem and applications, J. Diff. Eqns., 201(2004), 324-350.
331. M. Schechter, Z. Q. Wang and W. Zou, New linking theorem and signchanging solutions, Comm. in Partial Differential Eqnuations, 29(No. 3-4, 2004), 471-488.
332. M. Schechter and W. Zou, Infinitely many solutions to perturbed elliptic equations, J. Funct. Anal, 228(2005), 1-38.
333. M. Schechter and W. Zou, Sign-changing critical points from linking type theorems. Trans. AMS, (to appear).
334. E. Sere, Existence of infinitely many homoclinic orbits in Hamiltonian systems. Math. Z., 209(1992), 27-42.
335. E. Sere, Looking for the Bernoulli shift, Ann. Inst. H. Poincare, Analyse nonlineaire, 10 (1993), 561-590.
336. E. A. B. Silva, Critical point theorems and applications to differential equations, thesis, University of Wisconsin-Madison, 1988.
337. E. A. B. Silva, Linking theorems and applications to semilinear elliptic problems at resonance, Nonl Anal TMA, 16(1991), 455-477.
338. E. A. B. Silva, Existence and multiplicity of solutions for semilinear elliptic systems, NoDEA, 1(1994), 339-363.
339. E. A. B. Silva, Subharmonic solutions for subquadratic Hamiltonian systems, J. Differential Equations, 115(1995), 120-145.
340. E. A. B. Silva, Multiple critical points for asymptotically quadratic functional, Comm. in Partial Differential Equations, 21 (1996), 1729-1770.
341. E. A. B. Silva, Nontrivial solutions for noncooperative elliptic systems, Proc. USA-Chile Workshop on Nonlinear Analysis (Vina del Marvalparaiso, 2000). Electron. J. Diff. Eq. Conf, 6 (2001), 267-283.
342. E. A. B. Silva and M. S. Xavier, Multiplicity of solutions for quasilinear elliptic problems involving critical Sobolev exponents, Ann. Inst. H. Poincare Anal. Non Lineaire, 20 (2003), 341-358.
343. S. Smale, An infinite dimensional version of Sard's theorem, Amer. J. Math., 87(1965), 861-866.
344. S. Smale, Morse theory and a nonlinear generalization of Dirichlet Problem, Ann. of Math., 17(1964), 307-315.
345. S. Solimini, Morse index estimates in minimax theorems. Manuscript Math., 63(1989), 421-453.
346. E. H. Spanier, Algebraic topology, McGraw-Hill, New York, 1966.
347. A. H. Stone, Paracompactness and product space. Bull. Amer. Math. Soc, 54(1948), 977-982.
348. M. Struwe, Infinitely many critical points for functionals which are not even and applications to superlinear boundary value problems, manuscripta math., 32(1980), 335-364.
349. M. Struwe, Multiple solutions of differential equations without the Palais-Smale condition. Math. Ann., 261(1982), 399-412.
350. M. Struwe, Quasilinear elliptic eigenvalue problems, Gomm. Math. Helv., 58(1983), 509-527.
351. M. Struwe, The existence of surfaces of constant mean curvature with free boundaries, Acta Math., 160 (1988), 19-64.
352. M. Struwe, Variational Methods, Springer-Verlag, 1996.
353. C. A. Stuart, Bifurcation into spectral gaps. Bull. Belg. Math. Soc, Supplement, 1995.
354. C. A. Stuart and H. S. Zhou, A variational problem related to selftrapping of an electromagnetic field. Math. Methods in the Applied Scis., 19(1996), 1397-1407.
355. J. Su, Nontrivial periodic solutions for the asymptotically linear Hamiltonian systems with resonance at infinity, J. Differential Equations, 145(1998), 252-273.
356. A. Szulkin, Ljusternik-Schnirelman theory on C1-mainfolds, Ann. Inst. H. Poincare Anal. Non Lineaire, 5(1988), 119-139.
357. A. Szulkin, Cohomology and Morse theory for strongly indefinite functional. Math. Z., 209(1992), 375-418.
358. A. Szulkin, Index theories for indefinite functionals and applications. In: Topological and Variational Methods for Nonlinear Boundary Value Problems, P. Drabek ed.. Pitman Research Notes in Math. Ser. 365, Harlow, Essex 1997, 89-121.
359. A. Szulkin and M. Willem, Eigenvalue problems with indefinite weight, Studia Mathematica, 135(1999), 191-201.
360. A. Szulkin and W. Zou, Infinite dimensional cohomology groups and periodic solutions of asymptotically linear Hamiltonian systems, J. Diff. Eqns., 174(2001), 369-391.
361. A. Szulkin and W. Zou, Homoclinic orbit for asymptotically linear Hamiltonian Systems, J. Function Analysis, 187(2001), 25-41.
362. G. Talenti, Best constants in Sobolev inequality, Ann. Math., 110(1976), 353-372.
363. K. Tanaka, Homoclinic orbits in a first order superquadratic Hamiltonian system: Convergence of subharmonic orbits, J. Diff. Eqns., 94 (1991), 315-339.
364. K. Tanaka, Morse indices at critical points related to the symmetric mountain pass theorem and applications, Comm. in Partial Diff. Eqns., 14(1989), 99-128.
365. K. Tanaka, Infinitely many periodic solutions for the equation: Uu - Uxx uP-u = f{x, t), II, Trans. Amer. Math. Soc, 307(1988), 615-645.
366. M. E. Taylor, Partial differential equations III, Nonlinear Equation, Springer-Verlag, 1996.
367. H. T. Tehrani, Infinitely many solutions for indefinite semilinear elliptic equations without symmetry, Comm. Partial Differential Equations, 21(1996), 541-557.
368. H. T. Tehrani, H1 versus C1 local minimizers on manifolds, Nonl. Anal. TMA, 26(1996), 1491-1509.
369. J. Thayer, Operadores Auto-Adjuntos e Equacoes Diferenciais Parciais, Projecto Euclides, IMPA, 1987.
370. F. A. van Heerden, Multiple solutions for a Schrodinger type equation with an asymptotically linear term, Nonl. Anal. TMA, 55(2003), 739-758.
371. F. A. van Heerden and Z. Q. Wang, Schrodinger type equations with asymptotically linear nonlinear it ies. Differential Integral Equations, 16(2003), 257-280.
372. C. Troestler and M. Willem, Nontrivial solution of a semilinear Schrodinger equation, Comm. in Partial Differential Equations, 21(1996), 1431-1449.
373. Z. Q. Wang, On a superlinear elliptic equation, Ann. Inst. H. Poincare Anal. Non Lineaire, 8 (1991), 43-58.
374. Z. Q. Wang, Sign-changing solutions for a class of nonlinear elliptic problems. Progress in nonlinear analysis (Tianjin, 1999), 370-383, Nankai Ser. Pure Appl. Math. Theoret. Phys., 6, World Sci. Publishing.
375. Z. Q. Wang, Nonlinear boundary value problems with concave nonlinearities near the origin, NoDEA, 8(2001), 15-33.
376. M. Willem, Lectures on critical point theory. Fund. Universidade de Brasilia, No. 199, 1983.
377. M. Willem, Minimax Theorems, Birkhduser Boston, 1996.
378. M. Willem and W. Zou, On a semilinear Dirichlet problem and a nonlinear Schrodinger equation with periodic potential, Indiana Univ. Math. J., 52(2003), 109-132.
379. E. Zeidler, Nonlinear functional analysis and its applications, I-III, Springer-Verlag, 1985.
380. E. Zeidler, The Ljusternik-Schnirelman theory for indefinite and not necessarily odd nonlinear operators and its applications, Nonl. Anal. TMA, 4(1980), 451-489.
381. E. Zeidler, Ljusternik-Schnirelman theory on general level sets. Math. Nachr., 129(1986), 235-259.
382. Z. Zhang and S. Li, On sign-changing and multiple solutions of the p-Laplacian, J. Fund. Anal, 197 (2003), 447-468.
383. C. Zhong, X. Fan and W. Chen, Nonlinear functional analysis, Lan Zhou Univ. Press, 1998(in Chinese).
384. H. S. Zhou, Positive solution for a semilinear elliptic equation which is almost linear at infinity, Z. Angew. Math. Phys., 49(1998), 896-906.
385. W. Zou, Variant fountain theorems and their applications, Manuscripta Mathematica, 104(2001), 343-358.
386. W. Zou, Solitary waves of the generalized Kadomtsev-Petviashvili equations, Appl. Math. Letter., 15(2002), 35-39.
387. W. Zou, Multiple solutions for asymptotically linear elliptic systems, J. Math. Anal. Appl, 255(2001), 213-229.
388. W. Zou, Sign-changing critical point theory, preprint.
389. W. Zou, Computations of cohomology groups and applications to asymptotically linear beam equations and noncooperative elliptic systems, Comm. in Partial Differential Equations, 27(2002), 115-148.
390. W. Zou, Sign-changing saddle point, J. Funct. Anal., 219(2005), 433-468.
391. W. Zou, On finding sign-changing solutions, J. Funct. Anal, (in press).
392. W. Zou, Multiple solutions results for two-point boundary value problem with resonance both at origin and at infinity via computation of the critical groups. Discrete and Continuous Dynamic Systems, 4(1998), 485-496.
393. W. Zou, Computations of the critical groups and the nontrivial solutions for resonant type asymptotically linear Hamiltonian systems. Nonlinear Analysis, TMA, 49(4)(2002), 481-499.
394. W. Zou and S. Li, Infinitely many solutions for two classes of the second order Hamiltonian systems, J. Differential Equations, 186(2002) 141-164.
395. W. Zou and S. Li, New linking theorem and elliptic systems with nonlinear boundary condition, Nonl Anal TMA, 52(2003), 1797-1820.
396. W. Zou and J. Liu, Multiple solutions for elliptic resonant problem via local linking theory and Morse theory, J. Diff. Eqns., 170(2001), 68-95.