An obstacle problem for nonlinear hemivariational inequalities at resonance

Journal of Mathematical Analysis and Applications

Volumn 276, Issue 1, 2002, Pages 292-313

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

^a NATIONAL TECHNICAL UNIVERSITY OF ATHENS   (Greece)

Author keywords

Critical point; Generalized subdifferential; Hemivariational inequality at resonance; Locally Lipschitz function; Lower solution; Nonsmooth C condition; Obstacle; p Laplacian; Principal eigenvalue; Rayleigh quotient; Sobolev space

Indexed keywords

EID: 0036948341     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-247X(02)00443-2     Document Type: Article

References (25)

1. A. Anane, Simplicité et isolation de la première valeur propre du p-Laplacien avec poids, C. R. Acad. Sci. Paris Sér. I 305 (1987) 725-728.
2. D.D. Ang, K. Schmitt, V.K. Le, Noncoercive variational inequalities: some applications, Nonlinear Anal. 15 (1990) 497-512.
3. K.-C. Chang, Variational methods for nondifferentiable functionals and its applications to partial differential equations, J. Math. Anal. Appl. 80 (1981) 102-129.
4. F.H. Clarke, Optimization and Nonsmooth Analysis, Wiley, New York, 1983.
5. L. Evans, R. Gariepy, Measure Theory and Fine Properties of Functions, CRC Press, Boca Raton, 1992.
6. S. Hu, N.S. Papageorgiou, Handbook of Multivalued Analysis. Vol. I: Theory, Kluwer, Dordrecht, 1997.
7. S. Hu, N.S. Papagergiou, Handbook of Multivalued Analysis. Vol. II: Applications, Kluwer, Dordrecht, 2000.
8. S. Kesavan, Topics in Functional Analysis and Applications, Wiley, New York, 1989.
9. N. Kourogenis, N.S. Papageorgiou, Nonsmooth critical point theory and nonlinear elliptic equations at resonance, J. Austral. Math. Soc. Ser. A 69 (2000) 245-271.
10. S. Kyritsi, N.S. Papageorgiou, Nonsmooth critical point theory on closed convex sets and applications, J. Austral. Math. Soc. Ser. A, to appear.
11. V.K. Le, On global bifurcation of variational inequalities and applications, J. Differential Equations 141 (1997) 254-294.
12. V.K. Le, Existence of positive solutions of variational inequalities by a subsolution-supersolution approach, J. Math. Anal. Appl. 252 (2000) 65-90.
13. V.K. Le, Subsolution-supersolution method in variational inequalities, Nonlinear Anal. 45 (2001) 775-800.
14. V.K. Le, K. Schmitt, Minimization problems for noncoercive functionals subject to constraints, Trans. Amer. Math. Soc. 347 (1995) 4485-4513.
15. G.M. Lieberman, Boundary regularity for solutions of degenerate elliptic equations, Nonlinear Anal. 12 (1988) 1203-1219.
16. p-2u = 0, Proc. Amer. Math. Soc. 109 (1990) 157-164.
17. Z. Naniewicz, P. Panagiotopoulos, Mathematical Theory of Hemivariational Inequalities and Applications, Dekker, New York, 1995.
18. P. Panagiotopoulos, Hemivariational Inequalities: Applications to Mechanics and Engineering, Springer-Verlag, New York, 1993.
19. P. Quittner, Solvability and multiplicity results for variational inequalities, Comment. Math. Univ. Carolin. 30 (1989) 281-302.
20. R.E. Showalter, Monotone Operators in Banach Space and Nonlinear Partial Differential Equations, in: Math. Surveys Monographs, Vol. 49, AMS, Providence, RI, 1997.
21. M. Struwe, Variational Methods, Springer-Verlag, Berlin, 1990.
22. A. Szulkin, Positive solutions of variational inequalities: a degree theoretic approach, J. Differential Equations 57 (1985) 90-111.
23. A. Szulkin, Minimax principles for lower semicontinuous functions and applications to nonlinear boundary value problems, Ann. Inst. H. Poincaré, Anal. Non Lineaire 3 (1986) 77-109.
24. J.L. Vazquez, A strong maximum principle for some quasilinear elliptic equations, Appl. Math. Optim. 12 (1984) 191-202.
25. C.K. Zhong, On Ekeland's variational principle and a minimax theorem, J. Math. Anal. Appl. 205 (1997) 239-250.