Nonsmooth critical point theory on closed convex sets and nonlinear hemivariational inequalities

Nonlinear Analysis, Theory, Methods and Applications

Volumn 61, Issue 3, 2005, Pages 373-403

  Kyritsi, Sophia Th ^a   Papageorgiou, Nikolaos S ^a  

^a NATIONAL TECHNICAL UNIVERSITY OF ATHENS   (Greece)

Author keywords

Critical point; Critical value; Deformation result; Hemivariational inequality; Higher eigenvalues; Locally Lipschitz function; Lower solution; p Laplacian; Positive solution; Principal eigenvalue; Rayleigh quotient; Subdifferential; Upper solution

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; FUNCTION EVALUATION; MATHEMATICAL OPERATORS; SET THEORY; VARIATIONAL TECHNIQUES;

CRITICAL POINT; CRITICAL VALUE; DEFORMATION RESULT; HEMIVARIATIONAL INEQUALITY; HIGHER EIGENVALUES; LOCALLY LIPSCHITZ FUNCTION; LOWER SOLUTION; PRINCIPAL EIGENVALUE; RAYLEIGH QUOTIENT; UPPER SOLUTION;

NONLINEAR SYSTEMS;

EID: 14044253448     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2004.12.001     Document Type: Article

References (29)

1. A. Ambrosetti, and M. Badiale The dual variational principle and elliptic problems with discontinuities J. Math. Anal. Appl. 140 1989 363 373
2. A. Anane Simplicite et isolation de la premiere valeur propre du p -Laplacian avec poids C. R. Acad. Sci. Paris Ser. I, Math. 305 1987 725 728
3. A. Anane, and N. Tsouli On the second eigenvalue of the p -Laplacian Nonlinear Differential Equations (Fes 1994), Pitman Research Notes in Mathematics and Science vol. 343 1996 Longman Harlow, UK 1 9
4. K.-C. Chang Variational methods for nondifferentiable functionals and their applications to partial differential equations J. Math. Anal. Appl. 80 1981 102 129
5. F.-H. Clarke Optimization and Nonsmooth Analysis 1983 Wiley New York
6. J. Dugundji, and A. Granas Fixed Point Theory 1982 Polish Scientific Publishers Warsaw
7. L. Evans, and R. Gariepy Measure Theory and Fine Properties of Functions 1992 CRC Press Boca Raton, FL
8. L. Gasinski, and N.S. Papageorgiou Multiple solutions for nonlinear hemivariational inequalities near resonance Funkcial. Ekvac. 43 2000 271 284
9. L. Gasinski, and N.S. Papageorgiou An existence theorem for nonlinear hemivariational inequalities at resonance Bull. Austral. Math. Soc. 63 2001 1 14
10. L. Gasinski, N.S. Papageorgiou, Solutions and multiple solutions for quasilinear hemivariational inequalities at resonance, Proc. Roy. Soc. Edinburgh 131A (2001) 1-21.
11. D. Goeleven, D. Motreanu, and P. Panagiotopoulos Multiple solutions for a class of eigenvalue problems in hemivariational inequalities Nonlinear Anal. 29 1997 9 26
12. D. Goeleven, D. Motreanu, and P. Panagiotopoulos Eigenvalue problems for variational-hemivariational inequalities at resonance Nonlinear Anal. 33 1998 161 180
13. S. Hu, N.S. Papageorgiou, Handbook of Multivalued Analysis, vol. I: Theory, Kluwer, Dordrecht, The Netherlands, 1997.
14. S. Hu, N.S. Papageorgiou, Handbook of Multivalued Analysis, vol. II: Applications, Kluwer, Dordrecht, The Netherlands, 2000.
15. N. Kourogenis, and N.S. Papageorgiou Nonsmooth critical point theory and nonlinear elliptic equations at resonance J. Austral. Math. Soc. Ser. A 69 2000 245 271
16. O. Ladyzhenskaya, and N. Uraltsceva Linear and Quasilinear Elliptic Equations 1968 Academic Press New York
17. G. Lebourg, Valeur moyenne pour un gradient generalise, C. R. Acad. Sci. Paris, Ser. I, Math. t. 281, 795-797.
18. G.M. Lieberman Boundary regularity for solutions of degenerate elliptic equations Nonlinear Anal. 12 1988 1203 1219
19. P. Lindqvist On the equation div (∥ Dx ∥ p - 2 Dx) + λ | x | p - 2 x = 0 Proc. Amer. Math. Soc. 109 1990 157 164 (corrigenda Proc. Amer. Math. Soc. 116 (1992) 583-584)
20. I. Massabo Elliptic boundary value problems at resonance with discontinuous nonlinearities Boll. Un. Mat. Ital. 17-B 1980 1308 1320
21. Z. Naniewicz, and P. Panagiotopoulos Mathematical Theory of Hemivariational Inequalities and Applications 1995 Marcel Dekker New York
22. L. Nirenberg Variational methods in nonlinear problems M. Giaquinta Topics in Calculus of Variations, Lecture Notes in Mathematics vol. 1365 1987 Springer Berlin
23. P. Panagiotopoulos Hemivariational Inequalities. Applications to Mechanics and Engineering 1993 Springer New York
24. R.E. Showalter Hilbert Space Methods for Partial Differential Equations 1977 Pitman London
25. R.E. Showalter Monotone Operators in Banach Space and Nonlinear Partial Differential Equations, Mathematics Surveys and Monographs vol. 49 1997 AMS Providence, RI
26. M. Struwe Plateau's Problem and the Calculus of Variations, Mathematics Notes vol. 35 1989 Princeton University Press Princeton, NJ
27. M. Struwe Variational Methods 1990 Springer Berlin
28. C. Stuart Maximal and minimal solutions of elliptic differential equations with discontinuous non-linearities Math. Z. 163 1978 239 249
29. J.L. Vazquez A strong maximum principle for some quasilinear elliptic equations Appl. Math. Optim. 12 1984 191 202