Three Nontrivial Solutions for a Quasilinear Elliptic Differential Equation at Resonance with Discontinuous Right Hand Side

Journal of Mathematical Analysis and Applications

Volumn 238, Issue 2, 1999, Pages 477-490

  Kourogenis, Nikolaos C ^a   Papageorgiou, Nikolaos S ^a  

^a NATIONAL TECHNICAL UNIVERSITY OF ATHENS   (Greece)

Author keywords

Coercive functional; Critical point; Ekeland variational principle; Generalized subdifferential; Local minimum; Locally Lipschitz function; Nonsmooth mountain pass theorem; Nonsmooth Palais Smale condition; p Laplacian

Indexed keywords

EID: 0001215011     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.1999.6526     Document Type: Article

References (21)

1. R. Adams, "Sobolev Spaces," Academic Press, New York, 1975.
2. S. Ahmad, Multiple nontrivial solutions of resonant and nonresonant asymptotically linear problems, Proc. Amer. Math. Soc. 96 (1986), 405-409.
3. S. Ahmad, A. Lazer, A., and J. Paul, Elementary critical point theory and perturbation of elliptic boundary value problems at resonance, Indiana Univ. Math. J. 25 (1976), 933-944.
4. A. Ambrosetti and P. Rabinowitz, Dual variational methods in critical point theory and applications, J. Funct. Anal. 14 (1973), 349-381.
5. P. Bartolo, V. Benci, and D. Fortunato, Abstract critical point theorems and applications to some nonlinear problems with "strong resonance" at infinity, Nonlinear Anal. 9 (1983), 981-1022.
6. H. Brezis, "Analyse Fonctionelle," Masson, Paris, 1983.
7. K.-C. Chang, Variational methods for non-differentiable functionals and their applications to partial differential equations, J. Math. Anal. Appl. 80 (1981), 102-129.
8. F. H. Clarke, "Optimization and Nonsmooth Analysis," Wiley, New York, 1983.
9. I. J. Diaz, "Nonlinear Partial Differential Equations and Free Boundaries," Vol. 1, "Elliptic Problems," Pitman Research Notes in Mathematics, Vol. 106, Pitman, London, 1985.
10. J. Goncalves and O. Miyagaki, Multiple nontrivial solutions of semilinear strongly resonant elliptic equations, Nonlinear Anal. 19 (1992), 43-52.
11. J. Goncalves and O. Miyagaki, Three solutions for a strongly resonant elliptic problem, Nonlinear Anal. 24 (1995), 265-272.
12. S. Hu and N. S. Papageorgiou, "Handbook of Multivalued Analysis," Vol. I, "Theory," Kluwer, Dordrecht, 1997.
13. N. C. Kourogenis and N. S. Papageorgiou, Discontinuous quasilinear elliptic problems at resonance, Colloq. Math, 78 (1998), 213-223.
14. E. Landesman, S. Robinson, and A. Rumbos, Multiple solutions of semilinear elliptic problems at resonance, Nonlinear Anal. 24 (1995), 1049-1059.
15. p-2x = 0, Proc. Amer. Math. Soc. 109 (1990), 157-164.
16. R. Megginson, An Introduction to Banach Space Theory, Springer-Verlag, New York, 1998.
17. M. C. Pelisier and L. Reynaud, Etude d'un modèle mathematique d'écoulement de glacier, C. R. Acad. Sci. Paris Sér. A 279 (1979), 531-534.
18. P. Rabinowitz, "Minimax Methods in Critical Point Theory with Applications to Partial Differential Equations," CBMS, Vol. 65, Am. Math. Soc., Providence, 1986.
19. K. Thews, Nontrivial solutions of elliptic equations at resonance, Proc. Roy. Soc. Edinburgh Sect. A 85 (1990), 119-129.
20. P. Tolksdorf, Regularity for a more general class of quasilinear elliptic equations, J. Differential Equations 51 (1984), 126-150.
21. J. Ward, Applications of critical point theory to weakly nonlinear boundary value problems at resonance, Houston J. Math. 10 (1984), 291-305.