Nonsmooth critical point theory and nonlinear elliptic equations at resonance

Journal of the Australian Mathematical Society

Volumn 69, Issue 2, 2000, Pages 245-271

  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: 0040736083     PISSN: 14467887     EISSN: None     Source Type: Journal    
DOI: 10.1017/s1446788700002202     Document Type: Article

References (26)

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 and J. Paul, 'Elementary critical point theory and perturbations of elliptic boundary value problems at resonance', Indiana Univ. Math. J. 25 (1976), 933-944.
4. 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) 981-1012.
5. H. Brezis and L. Nirenberg, 'Remarks on finding critical points', Comm. Pure Appl. Math. 64 (1991), 939-963.
6. G. Cerami, 'Un criterio di esistenza per i punti critici su varieta illimitate', Rend. Instit. Lombardo Sci. Lett. 112 (1978), 332-336.
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. N. Ghoussoub, Duality and perturbation methods in critical point theory (Cambridge University Press, Cambridge, 1993).
10. J. Goncalves and O. Miyagaki, 'Multiple nontrivial solutions of semilinear strongly resonant elliptic equations', Nonlinear Anal. 19 (1992), 43-52.
11. _, 'Three solutions for a strongly resonant elliptic problems', Nonlinear Anal. 24 (1995), 265-272.
12. S. Hu and N. S. Papageorgiou, Handbook of multivalued analysis, volume I: theory (Kluwer, Dordrecht, 1997).
13. S. Kesavan, Topics in functional analysis and applications (Wiley, New York, 1989).
14. N. C. Kourogenis and N. S. Papageorgiou, 'Discontinuous quasilinear elliptic problems at resonance', Colloquium Math. 78 (1998), 213-223.
15. _, 'Multiple solutions for nonlinear discontinuous elliptic equations near resonance', Colloquium Math., to appear.
16. _, 'Multiple solutions for nonlinear discontinuous strongly resonant problems', J. Math. Soc. Japan, to appear.
17. _, 'Three nontrivial solutions for a quasilinear elliptic differential equation at resonance with discontinuous right hand side', J. Math. Anal. Appl. 238 (1999), 477-490.
18. E. Landesman, S. Robinson and A. Rumbos, 'Multiple solutions of semilinear elliptic problems at resonance', Nonlinear Anal. 24 (1995), 1045-1059.
19. G. Lieberman, 'Boundary regularity for solutions of degenerate elliptic equations', Nonlinear Anal. 12 (1988), 1203-1219.
20. p-2x = 0', Proc. Amer. Math. Soc. 109 (1990), 157-164.
21. P. Rabinowitz, Minimax methods in critical point theory with applications to partial differential equations, CBMS 65 (Amer. Math. Soc., Providence, 1986).
22. S. Solimini, 'On the solvability of some elliptic partial differential equations with linear part at resonance', J. Math. Anal. Appl. 117 (1986), 138-152.
23. K. Thews, 'Nontrivial solutions of elliptic equations at resonance', Proc. Roy. Soc. Edinburgh 85A (1990), 119-129.
24. P. Tolksdorf, 'Regularity for a more general class of quasilinear elliptic equations', J. Differential Equations 51 (1984), 126-150.
25. J. Ward, 'Applications of critical point theory to weakly nonlinear boundary value problems at resonance', Houston J. Math. 10 (1984), 291-305.
26. C.-K. Zhong, 'On Ekeland's variational principle and a minimax theorem', J. Math. Anal. Appl. 205 (1997), 239-250.