Quasilinear hemivariational inequalities with strong resonance at infinity

Nonlinear Analysis, Theory, Methods and Applications

Volumn 56, Issue 3, 2004, Pages 331-345

  Filippakis, Michael E ^a   Gasinski, Leszek ^b   Papageorgiou, Nikolaos S ^a  

^a NATIONAL TECHNICAL UNIVERSITY OF ATHENS   (Greece)

^b JAGIELLONIAN UNIVERSITY   (Poland)

Author keywords

Clarke subdifferential; Hemivariational inequality; Locally Lipschitz function; Nonsmooth critical point theory; p Laplacian; Principal eigenvalue; Strong resonance

Indexed keywords

ASYMPTOTIC STABILITY; DIFFERENTIAL EQUATIONS; EIGENVALUES AND EIGENFUNCTIONS; FUNCTIONS; PROBLEM SOLVING; THEOREM PROVING;

CLARKE SUBDIFFERENTIAL; HEMIVARIATIONAL INEQUALITY; LIPSCHITZ FUNCTIONS; NONSMOOTH CRITICAL POINT THEORY; STRONG RESONANCE;

NONLINEAR EQUATIONS;

EID: 0346340797     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2003.09.011     Document Type: Article

References (23)

1. Ahmad S., Lazer A., Paul J. Elementary critical point theory and perturbations of elliptic boundary value problems at resonance. Indiana Univ. Math. J. 25:1976;933-944.
2. Ambrosetti A., Mancini G. Theorems of existence and multiplicity for nonlinear elliptic problems with noninvertible linear part. Ann. Scuola Norm. Sup. Pisa. 5:1978;15-38.
3. Bartolo P., Benci V., Fortunato D. Abstract critical point theorems and applications to some nonlinear problems with "strong" resonance at infinity. Nonlinear Anal. 7:1983;981-1012.
4. Chang K.C. Variational methods for nondifferentiable functionals and their applications to partial differential equations. J. Math. Anal. Appl. 80:1981;102-129.
5. Clarke F.H. Optimization and Nonsmooth Analysis. 1983;Wiley, New York.
6. Denkowski Z., Migórski S., Papageorgiou N.S. An Introduction to Nonlinear Analysis: Theory. 2003;Kluwer/Plenum, New York.
7. Denkowski Z., Migórski S., Papageorgiou N.S. An Introduction to Nonlinear Analysis: Applications. 2003;Kluwer/Plenum, New York.
8. Gasiński L., Papageorgiou N.S. An existence theorem for nonlinear hemivariational inequalities at resonance. Bull. Aust. Math. Soc. 63:2001;1-14.
9. Gasiński L., Papageorgiou N.S. Solutions and multiple solutions for quasilinear hemivariational inequalities at resonance. Proc. R. Soc. Edinburgh, Sect. A, Mathematics. 131A:2001;1091-1111.
10. Goeleven D., Motreanu D., Panagiotopoulos P.D. Eigenvalue problems for variational-hemivariational inequalities at resonance. Nonlinear Anal. 33:1998;161-180.
11. Goncalves J., Miyagaki O. Three solutions for a strong resonant elliptic problem. Nonlinear Anal. 24:1995;265-272.
12. Hess P. Nonlinear perturbations of linear elliptic and parabolic problems at resonance. existence of multiple solutions Ann. Scuola Normale Sup. Pisa. 5:1978;527-537.
13. Hu S., Papageorgiou N.S. Handbook of multivalued analysis. Vol. II: Applications. 2000;Kluwer, Dordrecht, The Netherlands.
14. Kyritsi S., Papageorgiou N.S. Nonlinear hemivariational inequalities with the potential crossing the first eigenvalue. Bull. Aust. Math. Soc. 64:2001;381-393.
15. Landesman E., Lazer A. Nonlinear perturbations of linear elliptic boundary value problems at resonance. J. Math. Mech. 19:1970;609-623.
16. Motreanu D., Panagiotopoulos P.D. On the eigenvalue problem for hemivariational inequalities. existence and multiplicity of solutions J. Math. Anal. Appl. 197:1996;75-89.
17. Naniewicz Z., Panagiotopoulos P.D. Mathematical Theory of Hemivariational Inequalities and Applications. 1995;Marcel-Dekker, New York.
18. Panagiotopoulos P.D. Hemivariational Inequalities: Applications to Mechanics and Engineering. 1993;Springer, New York.
19. Rabinowitz P. Some minimax theorems and applications to nonlinear partial differential equations. Cesari L., Kannan R., Weinberger H. Nonlinear Analysis: A Collection of Papers in honor of E. Röthe. 1978;161-177 Academic Press, New York.
20. Szulkin A. Minimax principles for lower semicontinuous functions and applications to nonlinear boundary value problems. Ann. Inst. H. Poincaré. Anal. Non Lineaire. 3:1986;77-109.
21. Thews K. Nontrivial solutions of elliptic equations at resonance. Proc. R. Soc. Edinburgh. 85A:1980;119-129.
22. Ward J. Applications of critical point theory to weakly nonlinear boundary value problems at resonance. Houston J. Math. 10:1984;291-305.
23. Zhong C.K. On Ekeland's variational principle and a minimax theorem. J. Math. Anal. Appl. 205:1997;239-250.