Nonsmooth critical point theory and nonlinear elliptic equations at resonance

Kodai Mathematical Journal

Volumn 23, Issue 1, 2000, Pages 108-135

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

^a NATIONAL TECHNICAL UNIVERSITY OF ATHENS   (Greece)

Author keywords

First eigenvalue; Linking; Locally lipschitz function; Mountain pass theorem; Nonsmooth cerami condition; Nonsmooth critical point theory; Nonsmooth palais Smale condition; P Laplacian; Problems at resonance; Saddle point theorem; Subdifferential

Indexed keywords

EID: 85009868760     PISSN: 03865991     EISSN: None     Source Type: Journal    
DOI: 10.2996/kmj/1138044160     Document Type: Article

References (26)

1. Adams, R., Sobolev Spaces, Academic Press, New York, 1975.
2. Ahmad, S., Multiple nontrivial solutions of resonant and nonresonant asymptotically linear problems, Proc. Amer. Math. Soc, 96 (1986), pp. 405-409.
3. Ahmad, S., Lazer, A. and Paul, J., Elementary critical point theory and perturbations of elliptic boundary value problems at resonance, Indiana Univ. Math. J., 25 (1976), pp. 933-944.
4. Bartolo, P., Benci, V and Fortunato, D., Abstract critical point theorems and applications to some nonlinear problems with “strong resonance” at infinity, Nonlinear Appl., 9 (1983), pp. 981-1012.
5. Brezis, H. and Nirenberg, L., Remarks on finding critical points, Comm. Pure Appl. Math., 64 (1991), pp. 939-963.
6. Cerami, G., Un criterio di esistenza per 1 punti critici su varieta illimitate, Rend. Institute Lombardo Sci. Lett., 112 (1978) pp. 332-336.
7. Chang, K.-C, Variational methods for non-differentiable functionals and their applications to partial differential equations, J. Math. Anal. Appl., 80 (1981), pp. 102-129.
8. Clarke, F H., Optimization and Nonsmooth Analysis, Wiley, New York, 1983.
9. Ghoussoub, N., Duality and Perurbation Methods in Critical Point Theory, Cambridge University Press, Cambridge, 1993.
10. Goncalves, J. and Miyagaki, O., Multiple nontrivial solutions of semilinear strongly resonant elliptic equations, Nonlinear Anal., 19 (1992), pp. 43-52.
11. Goncalves, J. and Miyagaki, O., Three solutions for a strongly resonant elliptic problems, Nonlinear Anal., 24 (1995), pp. 265-272.
12. Hu, S. and Papageorgiou, N. S., Handbook of Multivalued Analysis, Volume 1: Theory, Kluwer, Dordrecht, 1997.
13. Kesavan, S., Topics in Functional Analysis and Applications, Wiley, New York, 1989.
14. Kourogenis, N. C. and Papageorgiou, N. S., Discontinuous quasilinear elliptic problems at resonance, Colloq. Math., 78 (1998), pp. 213-223.
15. Kourogenis, N. C. and Papageorgiou, N. S., Multiple solutions for nonlinear discontinuous elliptic equations near resonance, Colloq. Math., 81 (1999), pp. 80-99.
16. Kourogenis, N. C. and Papageorgiou, N. S., Three nontrivial solutions for a quasilinear elliptic differential equation at resonance with discontinuous right hand side, J. Math. Anal. Appl., 238 (1999), pp. 477-490.
17. Kourogenis, N. C. and Papageorgiou, N. S., Multiple solutions for nonlinear discontinuous strongly resonant problems, to appear in J. Math. Soc. Japan.
18. Landesman, E., Robinson, S. and Rumbos, A., Multiple solutions of semilinear elliptic problems at resonance, Nonlinear Anal., 24 (1995), pp. 1049-1059.
19. Lieberman, G., Boundary regularity for solutions of degenerate elliptic equations, Nonlinear Anal., 12 (1988), pp. 1203-1219.
20. 2x = 0, Proc. Amer. Math. Soc, 109 (1990), pp. 157-164.
21. Rabinowitz, P., Minimax Methods in Critical Point Theory with Applications to Differential Equations, CBMS Regional Conf. Ser. in Math., 65, Amer. Math. Soc, Providence, R. I., 1986.
22. Solimini, S., On the solvability of some elliptic partial differential equations with linear part at resonance, J. Math. Anal. Appl., 117 (1986), pp. 138-152.
23. Thews, K., Nontrivial solutions of elliptic equations at resonance, Proc. Royal Soc. Edinburgh Sect. A, 85 (1990), pp. 119-129.
24. Tolksdorf, P., Regularity for a more general class of quasilinear elliptic equations, J. Differential Equations, 51 (1984), pp. 126-150.
25. Ward, J., Applications of critical point theory to weakly nonlinear boundary value problems at resonance, Houston J. Math., 10 (1984), pp. 291-305.
26. Zhong, C.-K., On Ekeland’s variational principle and a minimax theorem, J. Math. Anal. Appl, 205 (1997), pp. 239-250.