Nontrivial solutions for p-Laplace equations with right-hand side having p-linear growth at infinity

Communications in Partial Differential Equations

Volumn 30, Issue 7-9, 2005, Pages 1191-1203

  Cingolani, Silvia ^a   Degiovanni, Marco ^b  

^a POLITECNICO DI BARI   (Italy)

^b UNIVERSITÀ CATTOLICA DEL SACRO CUORE   (Italy)

Author keywords

Cohomological index; Morse theory; Nontrivial solutions; p Laplace operator

Indexed keywords

EID: 27744499006     PISSN: 03605302     EISSN: 15324133     Source Type: Journal    
DOI: 10.1080/03605300500257594     Document Type: Article

References (25)

1. Amann, H., Zehnder, E. (1980). Nontrivial solutions for a class of nonresonance problems and applications to nonlinear differential equations. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 7(4):539-603.
2. Anane, A. (1987). Simplicité et isolation de la première valeur propre du p-laplacien avec poids. C. R. Acad. Sci. Paris Sér. I Math. 305(16):725-728.
3. Anane, A., Tsouli, N. (1996). On the second eigenvalue of the p-Laplacian. In: Nonlinear Partial Differential Equations. Pitman Res. Notes Math. Ser. (Fès, 1994), 343. Harlow: Longman, pp. 1-9.
4. Chang, K. C. (1981). Solutions of asymptotically linear operator equations via Morse theory. Comm. Pure Appl. Math. 34(5):693-712.
5. Chang, K. C. (1993). Infinite-dimensional Morse theory and multiple solution problems. Progress in Nonlinear Differential Equations and their Applications, 6. Boston: Birkhäuser.
6. Cingolani, S., Vannella, G. (2003a). Critical groups computations on a class of Sobolev Banach spaces via Morse index. Ann. Inst. H. Poincaré Anal. Non Linéaire 20(2): 271-292.
7. Cingolani, S., Vannella, G. (2003b). Morse index computations for a class of functionals defined in Banach spaces. In: Lupo, D., Pagani, C., Ruf, B., eds. Nonlinear Equations: Methods, Models and Applications. Progr. Nonlinear Differential Equations Appl. 54. (Bergamo, 2001). Boston: Birkhäuser, pp. 107-116.
8. Cingolani, S., Vannella, G. (2007). Marino-Prodi perturbation type results and Morse indices of minimax critical points for a class of functionals in Banach spaces. Annali di Matematica Pura ed Applicata,186(1),155-183.
9. Cuesta, M. (2001). Eigenvalue problems for the p-Laplacian with indefinite weights. Electron. J. Differential Equations 33:9.
10. Degiovanni, M. (2003). On Morse theory for continuous functionals. Conf. Semin. Mat. Univ. Bari 290, Aracane, Rome.
11. p-2u′)′ + f(t,u) = 0, u(0) = u(T) = 0, p > 1. J. Differential Equations 80(1): 1-13.
12. Drábek, P., Robinson, S. B. (1999). Resonance problems for the p-Laplacian. J. Funct. Anal. 169(1): 189-200.
13. Fadell, E. R., Rabinowitz, P. H. (1977). Bifurcation for odd potential operators and an alternative topological index. J. Func. Anal. 26(1):48-67.
14. Fadell, E. R., Rabinowitz, P. H. (1978). Generalized cohomological index theories for Lie group actions with an application to bifurcation questions for Hamiltonian systems. Invent. Math. 45(2): 139-174.
15. García Azorero, J., Peral Alonso, I. (1988). Comportement asymptotique des valeurs propres du p-laplacien. C. R. Acad. Sci. Paris Sér. I Math. 307(2):75-78.
16. Gromoll, D., Meyer, W. (1969). On differentiable functions with isolated critical points. Topology 8:361-369.
17. Guedda, M., Véron, L. (1989). Quasilinear elliptic equations involving critical Sobolev exponents. Nonlinear Anal. 13(8):879-902.
18. Lazer, A. C., Solimini, S. (1988). Nontrivial solutions of operator equations and Morse indices of critical points of min-max type. Nonlinear Anal. 12(8):761-775.
19. Lieberman, G. M. (1988). Boundary regularity for solutions of degenerate elliptic equations. Nonlinear Anal. 12(11):1203-1219.
20. p-2u = 0. Proc. Amer. Math. Soc. 109(1): 157-164.
21. Liu, J., Su, J. (2001). Remarks on multiple nontrivial solutions for quasi-linear resonant problems. J. Math. Anal. Appl. 258(1):209-222.
22. Marino, A., Prodi, G. (1975). Metodi perturbativi nella teoria di Morse. Boll. Un. Mat. Ital. (4) 11(3):suppl. 1-32.
23. Perera, K. (2003a). Nontrivial critical groups in p-Laplacian problems via the Yang index. Topol. Methods Nonlinear Anal. 21(2):301-309.
24. Perera, K. (2003b). Nontrivial solutions of p-superlinear p-Laplacian problems. Appl. Anal. 82(9):883-888.
25. Spanier, E. H. (1966). Algebraic Topology. New York: McGraw-Hill.