Multiplicity results for asymptotically linear elliptic problems at resonance

Journal of Mathematical Analysis and Applications

Volumn 278, Issue 2, 2003, Pages 397-408

  Su, Jiabao ^a  

^a CAPITAL NORMAL UNIVERSITY   (China)

Author keywords

Critical group; Critical point; Local linking; Morse theory; Resonance

Indexed keywords

EID: 0038066669     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-247X(02)00707-2     Document Type: Review

References (27)

1. H. Amann, E. Zehnder, Nontrivial solutions for a class of nonresonance problem and applications to nonlinear differential equations, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 7 (1980) 539-603.
2. P. Bartolo, V. Benci, D. Fortunato, Abstract critical point theorems and applications to nonlinear problems with "strong" resonance at infinity, Nonlinear Anal. 7 (1983) 981-1012.
3. T. Bartsch, S.J. Li, Critical point theory for asymptotically quadratic functionals and applications to problems with resonance, Nonlinear Anal. 28 (1997) 419-441.
4. 1 local minimizers, C. R. Acad. Sci. Paris 317 (1993) 465-475.
5. H. Brezis, L. Nirenberg, Remarks on finding critical points, Comm. Pure Appl. Math. 64 (1991) 939-963.
6. 1 isolated critical points, C. R. Acad. Sci. Paris 319 (1994) 441-446.
7. K.C. Chang, Infinite Dimensional Morse Theory and Multiple Solution Problems, Birkhäuser, Boston, 1993.
8. K.C. Chang, S.J. Li, J.Q. Liu, Remarks on multiple solutions for asymptotically linear elliptic boundary value problems, Topol. Methods Nonlinear Anal. 3 (1994) 179-187.
9. D.G. Costa, E.A. Silva, On a class of resonant problems at higher eigenvalues, Differential Integral Equations 8 (1995) 663-671.
10. D. Gromoll, W. Meyer, On differential functions with isolated point, Topology 8 (1969) 361-369.
11. E. Landesman, A.C. Lazer, Nonlinear perturbations of linear eigenvalue problems at resonance, J. Math. Mech. 19 (1970) 609-623.
12. E. Landesman, S. Robinson, A. Rumbos, Multiple solutions of semilinear elliptic problems at resonance, Nonlinear Anal. 24 (1995) 1049-1059.
13. S.J. Li, J.Q. Liu, Nontrivial critical point for asymptotically quadratic functions, J. Math. Anal. Appl. 165 (1992) 333-345.
14. S.J. Li, J.Q. Liu, Computations of critical groups at degenerate critical point and application to nonlinear differential equations with resonance, Houston J. Math. 25 (1999) 563-582.
15. S.J. Li, Z.Q. Wang, Mountain Pass Theorem in order intervals and multiple solutions for semilinear elliptic Dirichlet problems, J. d'Anal. Math. 81 (2000) 373-396.
16. S.J. Li, M. Willem, Multiple solutions for asymptotically linear boundary value problems in which the nonlinearity crosses at least one eigenvalue, Nonlinear Differential Equations Appl. 5 (1998) 479-490.
17. S.J. Li, M. Willem, Applications of local linking to critical point theory, J. Math. Anal. Appl. 189 (1995) 6-32.
18. S.J. Li, W.M. Zou, The computations of the critical groups with an application to elliptic resonant problems at higher eigenvalue, J. Math. Anal. Appl. 235 (1999) 237-259.
19. J.Q. Liu, A Morse index for a saddle point, Systems Sci. Math. Sci. 2 (1989) 32-39.
20. J. Mawhin, M. Willem, Critical Point Theory and Hamiltonian Systems, Springer-Verlag, Berlin, 1989.
21. K. Perera, Critical groups of critical points produced by local linking with applications, Abstr. Appl. Anal. 3 (1998) 437-446.
22. P. Rabinowitz, Minimax Methods in Critical Point Theory with Application to Differential Equations, in: CBMS, Vol. 65, Amer. Math. Soc., Providence, 1986.
23. M. Schechter, Elliptic resonance problems with unequal limits at infinity, Math. Ann. 300 (1994) 629-642.
24. M. Schechter, Bounded Resonance problem for semilinear elliptic equations, Nonlinear Anal. 24 (1995) 1471-1482.
25. J.B. Su, Semilinear elliptic resonant problems at higher eigenvalue with unbounded nonlinear terms, Acta Math. Sinica (N.S.) 14 (1998) 411-419.
26. J.B. Su, Semilinear elliptic boundary value problems with double resonance between two consecutive eigenvalues, Nonlinear Anal. 48 (6) (2002) 881-895.
27. J.B. Su, C.L. Tang, Multiplicity results for semilinear elliptic equations with resonance at higher eigenvalues, Nonlinear Anal. 44 (3) (2001) 311-321.