메뉴 건너뛰기




Volumn 354, Issue 8, 2002, Pages 3207-3227

Ljusternik-Schnirelman theory in partially ordered Hilbert spaces

Author keywords

Ljusternik Schnirelman theory; Minimax method; Order structure; Sign changing solutions

Indexed keywords


EID: 0036702017     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9947-02-03031-3     Document Type: Article
Times cited : (81)

References (50)
  • 1
    • 0030375718 scopus 로고    scopus 로고
    • Solutions of elliptic equations with indefinite nonlinearities via morse theory and linking
    • MR 96m:35091
    • S. Alama, M. Del Pino, Solutions of elliptic equations with indefinite nonlinearities via Morse theory and linking, Ann. Inst. H. Poincaré Analyse Non Linéaire 13(1996) 95-115. MR 96m:35091.
    • (1996) Ann. Inst. H. Poincaré Analyse Non Linéaire , vol.13 , pp. 95-115
    • Alama, S.1    Del Pino, M.2
  • 3
    • 0017014016 scopus 로고
    • Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces
    • MR 54:3519
    • H. Amann, Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces, SIAM Review, 18(1976) 620-709. MR 54:3519.
    • (1976) SIAM Review , vol.18 , pp. 620-709
    • Amann, H.1
  • 4
    • 0030577835 scopus 로고    scopus 로고
    • Multiplicity results for some nonlinear elliptic equations
    • MR 97b:35059
    • A. Ambrosetti, J. Garcia Azorero, I. Peral, Multiplicity results for some nonlinear elliptic equations, Jour. Funct. Anal. 137 (1996) 219-242. MR 97b:35059.
    • (1996) Jour. Funct. Anal. , vol.137 , pp. 219-242
    • Ambrosetti, A.1    Azorero, J.G.2    Peral, I.3
  • 6
    • 0000049245 scopus 로고
    • Combined effects of concave and convex nonlinearities in some elliptic problems
    • MR 95g:35059
    • A. Ambrosetti, H. Brezis, G. Cerami, Combined effects of concave and convex nonlinearities in some elliptic problems, Jour. Funct. Anal. 122(1994) 519-543. MR 95g:35059.
    • (1994) Jour. Funct. Anal. , vol.122 , pp. 519-543
    • Ambrosetti, A.1    Brezis, H.2    Cerami, G.3
  • 7
    • 34548350707 scopus 로고
    • Dual variational methods in critical point theory and applications
    • MR 51:6412
    • A. Ambrosetti, P. Rabinowitz, Dual variational methods in critical point theory and applications, Jour. Funct. Anal. 14(1973) 349-381. MR 51:6412.
    • (1973) Jour. Funct. Anal. , vol.14 , pp. 349-381
    • Ambrosetti, A.1    Rabinowitz, P.2
  • 8
    • 0035922965 scopus 로고    scopus 로고
    • Critical point theory on partially ordered Hilbert spaces
    • CMP 1 863 294
    • T. Bartsch, Critical point theory on partially ordered Hilbert spaces. J. Funct. Anal. 186 (2001), 117-152. CMP 1 863 294.
    • (2001) J. Funct. Anal. , vol.186 , pp. 117-152
    • Bartsch, T.1
  • 9
    • 0034400761 scopus 로고    scopus 로고
    • On the Morse indices of sign-changing solutions for nonlinear elliptic problems
    • MR 2001c:35079
    • T. Bartsch, K.C. Chang, Z.-Q. Wang, On the Morse indices of sign-changing solutions for nonlinear elliptic problems. Math. Zeit., 233 (2000), 655-677. MR 2001c:35079.
    • (2000) Math. Zeit. , vol.233 , pp. 655-677
    • Bartsch, T.1    Chang, K.C.2    Wang, Z.-Q.3
  • 10
    • 0000636235 scopus 로고    scopus 로고
    • On the existence of sign changing solutions for semilinear Dirichlet problems
    • MR 97m:35076
    • T. Bartsch, Z.-Q. Wang, On the existence of sign changing solutions for semilinear Dirichlet problems, Topological Meth. Nonlinear Anal., 7(1996) 115-131. MR 97m:35076.
    • (1996) Topological Meth. Nonlinear Anal. , vol.7 , pp. 115-131
    • Bartsch, T.1    Wang, Z.-Q.2
  • 11
    • 84990586507 scopus 로고
    • Remarks on finding critical points
    • MR 92i:58032
    • H. Brezis, L. Nirenberg, Remarks on finding critical points, Comm. Pure Appl. Math. 64(1991) 939-963. MR 92i:58032.
    • (1991) Comm. Pure Appl. Math. , vol.64 , pp. 939-963
    • Brezis, H.1    Nirenberg, L.2
  • 12
    • 0031372470 scopus 로고    scopus 로고
    • A sign changing solution for a superlinear Dirichlet problem
    • MR 99f:35056
    • A. Castro, J. Cossio, J.M. Neuberger, A sign changing solution for a superlinear Dirichlet problem, Rocky Mount. J. Math., 27 (1997), 1041-1053. MR 99f:35056.
    • (1997) Rocky Mount. J. Math. , vol.27 , pp. 1041-1053
    • Castro, A.1    Cossio, J.2    Neuberger, J.M.3
  • 13
    • 0001333845 scopus 로고    scopus 로고
    • A minmax principle, index of the critical point, and existence of sign-changing solutions to elliptic BVPs
    • MR 98j:35060
    • A. Castro, J. Cossio, J.M. Neuberger, A minmax principle, index of the critical point, and existence of sign-changing solutions to elliptic BVPs, Electron. J. Diff. Equations (1998), No. 2, 18 pp. MR 98j:35060.
    • (1998) Electron. J. Diff. Equations , vol.2 , pp. 18
    • Castro, A.1    Cossio, J.2    Neuberger, J.M.3
  • 14
    • 0001553624 scopus 로고    scopus 로고
    • Existence of many sign-changing nonradial solutions for semilinear elliptic problems on thin annuli
    • MR 2000j:35092
    • A. Castro, M. Finan, Existence of many sign-changing nonradial solutions for semilinear elliptic problems on thin annuli, Topological Meth. Nonlinear Anal. 13(1999), 273-279. MR 2000j:35092.
    • (1999) Topological Meth. Nonlinear Anal. , vol.13 , pp. 273-279
    • Castro, A.1    Finan, M.2
  • 15
    • 0000484583 scopus 로고
    • A variant mountain pass lemma
    • MR 85h:58037
    • K.C. Chang, A variant mountain pass lemma, Sci. Sinica Ser. A 26 (1983), no. 12, 1241-1255. MR 85h:58037.
    • (1983) Sci. Sinica Ser. A , vol.26 , Issue.12 , pp. 1241-1255
    • Chang, K.C.1
  • 16
    • 0011181771 scopus 로고
    • Variational methods and sub- and supersolutions
    • MR 85h:58038
    • K.C. Chang, Variational methods and sub- and supersolutions, Sci. Sinica Ser. A 26 (1983), no. 12, 1256-1265. MR 85h:58038.
    • (1983) Sci. Sinica Ser. A , vol.26 , Issue.12 , pp. 1256-1265
    • Chang, K.C.1
  • 19
    • 0000734186 scopus 로고
    • Some existence results for superlinear elliptic boundary value problems involving critical exponents
    • MR 88b:35074
    • G. Cerami, S. Solimini, M. Struwe, Some existence results for superlinear elliptic boundary value problems involving critical exponents, J. Funct. Anal., 69(1986), 289-306. MR 88b:35074.
    • (1986) J. Funct. Anal. , vol.69 , pp. 289-306
    • Cerami, G.1    Solimini, S.2    Struwe, M.3
  • 20
    • 0034215638 scopus 로고    scopus 로고
    • Algorithms and visualization for solutions of nonlinear elliptic equations
    • CMP 2001:01
    • G. Chen, W. Ni, J. Zhou, Algorithms and visualization for solutions of nonlinear elliptic equations, Internat. Jour. Bifur. Chaos Appl. Sci. Engrg., 10 (2000), 1565-1612. CMP 2001:01.
    • (2000) Internat. Jour. Bifur. Chaos Appl. Sci. Engrg. , vol.10 , pp. 1565-1612
    • Chen, G.1    Ni, W.2    Zhou, J.3
  • 21
    • 0002224090 scopus 로고
    • A variant of the Ljusternik-Schnirelman theory
    • MR 45:5836
    • D.C Clark, A variant of the Ljusternik-Schnirelman theory, Ind. Univ. Math. J. 22(1972) 65-74. MR 45:5836.
    • (1972) Ind. Univ. Math. J. , vol.22 , pp. 65-74
    • Clark, D.C.1
  • 22
    • 0000907310 scopus 로고
    • On the indices of fixed points of mappings in cones and applications
    • MR 84d:58020
    • E.N. Dancer, On the indices of fixed points of mappings in cones and applications, J. Math. Anal. Appl., 91(1983), 131-151. MR 84d:58020.
    • (1983) J. Math. Anal. Appl. , vol.91 , pp. 131-151
    • Dancer, E.N.1
  • 23
    • 0011182616 scopus 로고
    • Positivity of maps and applications, topological nonlinear analysis
    • Birkhäuser, Boston. MR 95m:47119
    • E.N. Dancer, Positivity of maps and applications, Topological Nonlinear Analysis, Progr. Nonlinear Differential Equations Appl., 15(1995) 303-340, Birkhäuser, Boston. MR 95m:47119.
    • (1995) Progr. Nonlinear Differential Equations Appl. , vol.15 , pp. 303-340
    • Dancer, E.N.1
  • 24
    • 0001421282 scopus 로고
    • On sign-changing solutions of certain semilinear elliptic problems
    • MR 97m:35061
    • E.N. Dancer, Y. Du, On sign-changing solutions of certain semilinear elliptic problems, Appl. Anal. 56 (1995), no. 3-4, 193-206. MR 97m:35061.
    • (1995) Appl. Anal. , vol.56 , Issue.3-4 , pp. 193-206
    • Dancer, E.N.1    Du, Y.2
  • 25
    • 0000521891 scopus 로고
    • Multiple solutions of some semilinear elliptic equations via the generalized conley index
    • MR 96a:35059
    • E.N. Dancer, Y. Du, Multiple solutions of some semilinear elliptic equations via the generalized Conley index, J. Math. Anal. Appl. 189 (1995), no. 3, 848-871. MR 96a:35059.
    • (1995) J. Math. Anal. Appl. , vol.189 , Issue.3 , pp. 848-871
    • Dancer, E.N.1    Du, Y.2
  • 26
    • 0000682754 scopus 로고    scopus 로고
    • The generalized conley index and multiple solutions of semilinear elliptic problems
    • MR 97i:35048
    • E.N. Dancer, Y. Du, The generalized Conley index and multiple solutions of semilinear elliptic problems, Abstract Appl. Anal., 1(1996) 103-135. MR 97i:35048.
    • (1996) Abstract Appl. Anal. , vol.1 , pp. 103-135
    • Dancer, E.N.1    Du, Y.2
  • 27
    • 0031175615 scopus 로고    scopus 로고
    • A note on multiple solutions of some semilinear elliptic problem
    • MR 98g:35075
    • E.N. Dancer, Y. Du, A note on multiple solutions of some semilinear elliptic problem, J. Math. Anal. Appl. 211(1997) 626-640. MR 98g:35075.
    • (1997) J. Math. Anal. Appl. , vol.211 , pp. 626-640
    • Dancer, E.N.1    Du, Y.2
  • 29
    • 0033201521 scopus 로고    scopus 로고
    • A high-linking algorithm for sign-changing solutions of semilinear elliptic equations
    • MR 2000d:65208
    • Z. Ding, D. Costa, G. Chen, A high-linking algorithm for sign-changing solutions of semilinear elliptic equations, Nonlinear Analysis, 38 (1999), 151-172. MR 2000d:65208.
    • (1999) Nonlinear Analysis , vol.38 , pp. 151-172
    • Ding, Z.1    Costa, D.2    Chen, G.3
  • 30
    • 0001388207 scopus 로고
    • Generalized cohomological index thoeries for lie group actions with an application to bifurcation questions for Hamiltonian systems
    • MR 57:17677
    • E. Fadell, P.H. Rabinowitz, Generalized cohomological index thoeries for Lie group actions with an application to bifurcation questions for Hamiltonian systems, Inv. Math., 45 (1978), 139-174. MR 57:17677.
    • (1978) Inv. Math. , vol.45 , pp. 139-174
    • Fadell, E.1    Rabinowitz, P.H.2
  • 31
    • 84968483586 scopus 로고
    • Multiplicity of solutions for elliptic problems with critical exponent or with a nonsymmetric term
    • MR 91g:35108
    • J. Garcia Azorero, I. Peral Alonso, Multiplicity of solutions for elliptic problems with critical exponent or with a nonsymmetric term, Trans. AMS. 323 (1991), 877 - 895. MR 91g:35108.
    • (1991) Trans. AMS. , vol.323 , pp. 877-895
    • Azorero, J.G.1    Alonso, I.P.2
  • 32
    • 0001327974 scopus 로고
    • Free Ljusternik-Schnirelman theory and the bifurcation diagrams of certain singular nonlinear systems
    • MR 88d:34020
    • H.P. Heinz, Free Ljusternik-Schnirelman theory and the bifurcation diagrams of certain singular nonlinear systems, J. Diff. Eqns. 263 - 300 (1987). MR 88d:34020.
    • (1987) J. Diff. Eqns. , vol.263-300
    • Heinz, H.P.1
  • 33
    • 0000835133 scopus 로고
    • Variational and topological methods in partially ordered Hilbert spaces
    • MR 84g:58030
    • H. Hofer, Variational and topological methods in partially ordered Hilbert spaces, Math. Ann. 261 (1982), 493 - 514. MR 84g:58030.
    • (1982) Math. Ann. , vol.261 , pp. 493-514
    • Hofer, H.1
  • 34
    • 84968468179 scopus 로고
    • A note on the topological degree at a critical point of mountain pass type
    • MR 85a:58015
    • H. Hofer, A note on the topological degree at a critical point of mountain pass type, Proc. AMS 90(1984) 309-315. MR 85a:58015.
    • (1984) Proc. AMS , vol.90 , pp. 309-315
    • Hofer, H.1
  • 36
    • 0000095715 scopus 로고    scopus 로고
    • Some aspects of semilinear elliptic boundary value problem
    • S.J. Li, Some aspects of semilinear elliptic boundary value problem, Progress in Nonlinear Analysis, (1999) 234-256.
    • (1999) Progress in Nonlinear Analysis , pp. 234-256
    • Li, S.J.1
  • 37
    • 0035047047 scopus 로고    scopus 로고
    • Multiple and sign-changing solutions of an elliptic eigenvalue problem with constraint
    • MR 2002b:35166
    • Y. Li, Z.L. Liu, Multiple and sign-changing solutions of an elliptic eigenvalue problem with constraint, Science in China (Series A), 44(2001), No.1, 48-57. MR 2002b:35166.
    • (2001) Science in China (Series A) , vol.44 , Issue.1 , pp. 48-57
    • Li, Y.1    Liu, Z.L.2
  • 38
    • 0011207903 scopus 로고
    • An abstract critical point theorem and applications
    • (Chinese) MR 88a:58036
    • S.J. Li, Z.-Q. Wang,. An abstract critical point theorem and applications, Acta Math. Sinica, 29(1986), 585-589. (Chinese) MR 88a:58036.
    • (1986) Acta Math.inica , vol.29 , pp. 585-589
    • Li, S.J.1    Wang, Z.-Q.2
  • 39
    • 0000776333 scopus 로고    scopus 로고
    • Mountain-pass theorem in order intervals and multiple solutions for semilinear elliptic Dirichlet problems
    • MR 2001h:35063
    • S.J. Li, 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. MR 2001h:35063.
    • (2000) J. d'Analyse Math. , vol.81 , pp. 373-396
    • Li, S.J.1    Wang, Z.-Q.2
  • 40
    • 0036289620 scopus 로고    scopus 로고
    • A minimax method for finding multiple critical points and its applications to semilinear PDEs
    • Y. Li and J. Zhou, A minimax method for finding multiple critical points and its applications to semilinear PDEs, SIAM J. Sci. Comput. 23 (2001), no. 3, 840-865.
    • (2001) SIAM J. Sci. Comput. , vol.23 , Issue.3 , pp. 840-865
    • Li, Y.1    Zhou, J.2
  • 41
    • 0001831970 scopus 로고    scopus 로고
    • A numerical method for finding sign-changing solutions of superlinear dirichlet problems
    • MR 98c:65200
    • J.M. Neuberger, A numerical method for finding sign-changing solutions of superlinear Dirichlet problems, Nonlinear World 4 (1997), 73-83. MR 98c:65200.
    • (1997) Nonlinear World , vol.4 , pp. 73-83
    • Neuberger, J.M.1
  • 42
    • 49949142757 scopus 로고
    • Lusternik-Schnirelman theory on Banach manifolds
    • MR 45:4184
    • R.S. Palais, Lusternik-Schnirelman theory on Banach manifolds, Topology, 5(1966), 1-16. MR 45:4184.
    • (1966) Topology , vol.5 , pp. 1-16
    • Palais, R.S.1
  • 43
    • 0343987648 scopus 로고
    • Some critical point theorems and applications to semilinear elliptic partical differential equations
    • MR 58:7695
    • P. Rabinowitz, Some critical point theorems and applications to semilinear elliptic partical differential equations, Ann. Scuola Norm. Sup. Pisa, Seri IV. 5 (1978) 215-223. MR 58:7695.
    • (1978) Ann. Scuola Norm. Sup. Pisa, Seri IV. , vol.5 , pp. 215-223
    • Rabinowitz, P.1
  • 44
    • 0001901435 scopus 로고
    • Minimax methods in critical point theory with applications to differential equations
    • American Mathematical Society, Providence, R.I., MR 87j:58024
    • P. Rabinowitz, Minimax Methods in Critical Point Theory with Applications to differential Equations, CBMS Reg. Conf. Ser. Math. 65, American Mathematical Society, Providence, R.I., (1986). MR 87j:58024.
    • (1986) CBMS Reg. Conf. Ser. Math. , vol.65
    • Rabinowitz, P.1
  • 45
    • 84972488097 scopus 로고
    • Nodal solutions of semilinear elliptic equations with critical exponent
    • MR 92k:35109
    • G. Tarantello, Nodal solutions of semilinear elliptic equations with critical exponent, Differential Integral Equations 5(1992), 25-42. MR 92k:35109.
    • (1992) Differential Integral Equations , vol.5 , pp. 25-42
    • Tarantello, G.1
  • 48
    • 0002823383 scopus 로고    scopus 로고
    • Nonlinear boundary value problems with concave nonlinearities near the origin
    • MR 2002c:35107
    • Z.-Q. Wang, Nonlinear boundary value problems with concave nonlinearities near the origin, NoDEA Nonlinear Diff. Equations Appl. 8(2001), 15-33. MR 2002c:35107.
    • (2001) NoDEA Nonlinear Diff. Equations Appl. , vol.8 , pp. 15-33
    • Wang, Z.-Q.1
  • 49
    • 0011253740 scopus 로고    scopus 로고
    • Sign-changing solutions for a class of nonlinear elliptic problems, nonlinear analysis
    • Eds. K.-C. Chang and Y. Long
    • Z.-Q. Wang, Sign-Changing Solutions for a Class of Nonlinear Elliptic Problems, Nonlinear Analysis(Eds. K.-C. Chang and Y. Long), Nankai Series in Pure and Applied Math. 6 (2000), 370-383.
    • (2000) Nankai Series in Pure and Applied Math. , vol.6 , pp. 370-383
    • Wang, Z.-Q.1
  • 50


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.