Multiple solutions to p- laplacian problems with asymptotic nonlinearity as up-1 at infinity

Journal of the London Mathematical Society

Volumn 65, Issue 1, 2002, Pages 123-138

  Li, Gongbao ^a   Zhou, Huan Song ^a  

^a Wuhan National Laboratory for Optoelectronics   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036337701     PISSN: 00246107     EISSN: 14697750     Source Type: Journal    
DOI: 10.1112/S0024610701002708     Document Type: Article

References (19)

1. H. Amann, ‘Saddle points and multiple solutions of differential equations’, Math. Z. 169 (1979) 127–166.
2. H. Amann and E. Zehnder, ‘Nontrivial solutions for a class of nonresonance problems and applications to nonlinear differential equations’, Ann. Scuola Norm. Sup. Pisa 7 (1980) 539–603.
3. A. Ambrosetti and P. Rabinowitz, ‘Dual variational methods in critical points theory and applications’, J. Funct. Anal. 14 (1973) 349–381.
4. A. Anane and J.-P. Gossez, ‘Strongly nonlinear elliptic problems near resonance’, Comm. Partial Differential Equations 15 (1990) 1141–1159.
5. P. Bartolo, V. Benci and D. Fortunato, ‘Abstract critical theorems and applications to some nonlinear problems with “strong” resonance at infinity’, Nonlinear Anal. 7 (1983) 981–1012.
6. A. Casro and A. C. Lazer, ‘Critical points theory and the number of solutions of nonlinear Dirichlet problem’, Ann. Mat. Pura Appl. 120 (1979) 114–137.
7. G. Cerami, ‘Un criterio de esistenza per i parti critici su varietà ilimitate’, Rc. Ist. Lomb. Sci. Lett. 112 (1978) 332–336.
8. K. C. Chang, ‘Solutions of asymptotically linear operator equations via Morse theory’, Comm. Pure Appl. Math. 34 (1981) 693–712.
9. D. G. Costa and C. A. Magalhães, ‘Existence results for perturbations of the p-Laplacian’, Nonlinear Anal. 24 (1995) 409–418.
10. P. Hess, ‘Nonlinear perturbations of linear elliptic and parabolic problems at resonance: existence of multiple solutions’, Ann. Scuola Norm. Sup. Pisa 5 (1978) 527–537.
11. E. A. Landsman and A. C. Lazer, ‘Nonlinear perturbation of linear elliptic boundary value problems at resonance’, J. Math. Mech. 19 (1970) 609–623.
12. G. B. Li and O. Martio, ‘Stability in obstacle problems’, Math. Scand. 75 (1994) 87–100.
13. G. B. Li and H. S. Zhou, ‘Asymptotically “linear” Dirichlet problem for p-Laplacian’, Nonlinear Anal. 43 (2001) 1043–1055.
14. G. B. Li and H. S. Zhou, ‘Dirichlet problem of p-Laplacian with nonlinear term f(x,u) ~ up-1 at infinity’, Morse theory, minimax theory and their applications to nonlinear partial differential equations (ed. H. Brezis, S. J. Li et al, International Press, to appear).
15. P. Lindqvist, ‘On a nonlinear eigenvalue problem’, Proceedings of Fall School in Analysis, Jyväskylä, 1994, 1995, 33–54 (ed. T. Kilpeläinen).
16. R. T. Shen and X. K. Guo, ‘Nontrivial critical points for the functional ∫Ω F(x, u, Du)dx’, Acta Math. Sci. 10 (1990) 249–258 (Chinese).
17. C. A. Stuart, ‘Self-trapping of an electromagnetic field and bifurcation from the essential spectrum’, Arch. Rational Mech. Anal. 113 (1991) 65–96.
18. C. A. Stuart, ‘Magnetic field wave equations for TM-modes in nonlinear optical waveguides’, Reaction diffusion systems (ed. Caristi and Mitidieri, Marcel Dekker, 1997) 377–400.
19. C. A. Stuart and H. S. Zhou, ‘Applying the mountain pass theorem to an asymptotically linear elliptic equation on RN’, Comm. Partial Differential Equations 24 (1999) 1731–1758.