Dirichlet problem with indefinite nonlinearities

Calculus of Variations and Partial Differential Equations

Volumn 20, Issue 3, 2004, Pages 257-282

  Chang, Kung Ching ^a   Jiang, Mei Yue ^a  

^a PEKING UNIVERSITY   (China)

Author keywords

Critical groups; Dirichlet problem; Indefinite nonlinearities

Indexed keywords

EID: 3042632099     PISSN: 09442669     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00526-003-0236-7     Document Type: Article

References (22)

1. Alama, S., Del Pino, M.: Solutions of elliptic equations with indefinite nonlinearities via Morse theory and linking. Ann. Inst. H. Poincaré, Anal. Nonlinéaire 13, 95-115 (1996)
2. Alama, S., Tarantello, G.: On semilinear elliptic equations with indefinite nonlinearities. Calc.Var. 1, 439-475 (1993)
3. Alama, S., Tarantello, G.: Elliptic problems with nonlinearities indefinite in sign. J. Funct. Anal. 141, 159-215 (1996)
4. Ambresetti, A., Rabinowitz, P.H.: Dual variational methods in critical point theory and applications. J. Funct. Anal. 14, 349-381 (1973)
5. Bartsch, T.: Critical point theory on partial ordered Hilbert spaces. J. Funct. Anal. 186, 117-152 (2001)
6. Bartsch, T., Chang, K.-C., Wang, Z.-Q.: On the Morse indices of sign changing solutions of nonlinear elliptic equations. Math. Z. 233, 655-677 (2000)
7. Bartsch, T., Wang, Z.-Q.: On the existence of sign changing solutions for semilinear Dirichlet problem. TMNA 7, 115-131 (1996)
8. Berestycki, H., Capuzzo-Dolcetta, I., Nirenberg, L.: Superlinear indefinite elliptic problem and nonlinear Liouville theorems. TMNA 4, 59-78 (1994)
9. Berestycki, H., Capuzzo-Dolcetta, I., Nirenberg, L.: Variational methods for indefinite superlinear homogeneous elliptic problems. NoDEA 2, 533-572 (1995)
10. Chang, K.-C.: Infinite Dimensional Morse Theory and Multiple Solution Problems. Birkhäuser, Boston 1993
11. 1 isolated critical points. C. R. Acad. Sci. Paris 319, 441-446 (1994)
12. Chang, K.-C., Ghoussoub, N.: The Conley index and the critical groups via an extension of Gromoll-Meyer theory. TMNA 7, 77-93 (1996)
13. Li, S.-J., Liu, J.-Q.: Computations of critical groups at degenerate critical point and applications to nonlinear differential equation with resonance. Houston Math. J. 25, 563-582 (1999)
14. Li, S.-J., Wang, Z.-Q.: Mountain pass theorem in order interval and multiple solutions for semilinear elliptic Dirichlet problems. J. d'Analyses Math. 81, 373-396 (2000)
15. Li, S.-J., Wang, Z.-Q.: Liusternik-Schnirelman theory in partial ordered Hilbert spaces. Trans. Amer. Math. Soc. 354, 3207-3227 (2002)
16. Liu, J.-Q., Wu, S.-P.: Calculating critical groups of solutions for elliptic problem with jumping nonlinearity. Nonlinear Anal., Ser. A: Theory Methods 49, 779-797 (2001)
17. Perera, K., Schechter, M.: Solution of nonlinear equations having asymptotic limits at zero and infinity. Calc. Var. 12, 359-369 (2001)
18. Rabinowitz, P.H.: Minimax Methods in Critical Point Theory with Applications to Differential Equations. CBMS, Regional Conf. Ser. in Math., 65, Amer. Math. Soc., Providence, RI, 1986
19. Ramos, M., Terracini, S., Troester, C.: Superlinear indefinite elliptic problems and Pohozaev type identities. J. Funct. Anal. 159, 596-628 (1998)
20. Wang, Z.-Q.: On a superlinear elliptic equation. Ann. Inst. H. Poincaré, Anal. Nonlinéaire 8, 43-57 (1991)
21. Benci, V.: Introduction to Morse Theory: A New Approach. Matzen, M., Vignoli A. (eds.) Topological Nonlinear Analysis, pp. 37-177. Birkhäuser, Boston 1995
22. Zou, W., Li, S.-J.: Infinitely many solutions for Hamiltonian systems. J. Differential Equations 186, 141-164 (2002)