Superlinear Indefinite Elliptic Problems and Pohoz′aev Type Identities

Journal of Functional Analysis

Volumn 159, Issue 2, 1998, Pages 596-628

  Ramos, Miguel ^a   Terracini, Susanna ^b   Troestler, Christophe ^c  

^a UNIVERSITY OF LISBON   (Portugal)

^b POLITECNICO DI MILANO   (Italy)

^c UNIVERSITY OF MONS   (Belgium)

Author keywords

Minimax methods; Morse theory; Superlinear elliptic problems

Indexed keywords

EID: 0001366532     PISSN: 00221236     EISSN: None     Source Type: Journal    
DOI: 10.1006/jfan.1998.3332     Document Type: Article

References (19)

1. Alama S., Tarantello G. On semilinear elliptic equations with indefinite nonlinearities. Cal. Var. Partial Differential Equations. 1:1993;439-475.
2. S. Alama, G. Tarantello, Elliptic problems with nonlinearities indefinite in sign, 1994.
3. S. Alama, M. Del Pino, Solutions of elliptic equations with indefinite nonlinearities via Morse theory and linking, 1995.
4. M. Badiale, Infinitely many solutions for some indefinite nonlinear elliptic problems, 1995.
5. M. Badiale, E. Nabana, A remark on multiplicity of solutions for semi-linear elliptic problems with indefinite nonlinearity, 1995.
6. Bahri A., Lions P. L. Solutions of superlinear elliptic equations and their Morse indices. Comm. Pure Appl. Math. 45:1992;1205-1215.
7. Berestycki H., Capuzzo Dolcetta I., Nirenberg L. Superlinear indefinite elliptic problems and nonlinear Liouville theorems. Topol. Methods Nonlinear Anal. 4:1994;59-78.
8. Berestycki H., Capuzzo Dolcetta I., Nirenberg L. Variational methods for indefinite superlinear homogeneous elliptic systems. NoDEA. 2:1995;533-572.
9. Butler G. J. Rapid oscillation, nonextendability, and the existence of periodic solutions to second order nonlinear ordinary differential equations. J. Differential Equations. 22:1976;467-477.
10. Gidas B., Spruck J. A priori bounds for positive solutions of nonlinear elliptic equations. Comm. Partial Differential Equations. 6:1981;883-901.
11. Gilbarg D., Trudinger N. S. Elliptic Partial Differential Equations of Second Order. 1983;Springer-Verlag, Berlin/New York.
12. Kavian O. Introduction à la Théorie des Points Critiques et Applications aux Problèmes Elliptiques. 1993;Springer-Verlag, Berlin/New York.
13. Lazer A. C., Solimini S. Nontrivial solutions of operator equations and Morse indices of critical points of min-max type. Nonlinear Anal. 12:1988;761-775.
14. Liu J. Q., Li S. Some existence theorems on multiple critical points and their applications. Kexue Tongbao Chinese. 17:1984.
15. Li S., Willem M. Applications of local linking to critical point theory. J. Math. Anal. Appl. 189:1995;6-32.
16. M. Ramos, Linking theorems in critical point theory, University of Lisbon, 1993.
17. Ramos M., Sanchez L. Homotopical linking and Morse index estimates in min-max theorems. Manuscripta Math. 87:1995;269-284.
18. Ramos M., Terracini S., Troesler C. Problèmes elliptiques surlinéaires avec nonlinéarité sans signe défini. C. R. Acad. Sci. Paris Sér. I. 35:1997;283-286.
19. Willem M. Minimax Theorems. Progr. Nonlinear Differential Equations Appl. 24:1996;Birkhäuser, Boston.