Three critical points for perturbed nonsmooth functionals and applications

Nonlinear Analysis, Theory, Methods and Applications

Volumn 72, Issue 3-4, 2010, Pages 1319-1338

  Iannizzotto, Antonio ^a  

^a UNIVERSITY OF CATANIA   (Italy)

Author keywords

Nonsmooth critical point theory; Topological minimax theory; Variational hemivariational inequalities

Indexed keywords

CRITICAL POINTS; FUNCTIONALS; MINIMAX INEQUALITY; MINIMAX THEORY; MULTIPLICITY RESULTS; NON-SMOOTH; NONSMOOTH CRITICAL POINT THEORY; TWO PARAMETER; VARIATIONAL-HEMIVARIATIONAL INEQUALITY;

EQUATIONS OF STATE; GALLIUM;

NONLINEAR ANALYSIS;

EID: 71549158802     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2009.08.001     Document Type: Article

References (33)

1. Ricceri B. On a three critical points theorem. Arch. Math. (Basel) 75 (2000) 220-226
2. Ricceri B. A three critical points theorem revisited. Nonlinear Anal. 70 (2009) 3084-3089
3. Marano S.A., and Motreanu D. On a three critical points theorem for non-differentiable functions and applications to nonlinear boundary value problems. Nonlinear Anal. 48 (2002) 37-52
4. Bonanno G., and Candito P. On a class of nonlinear variational-hemivariational inequalities. Appl. Anal. 83 (2004) 1229-1244
5. Kristály A. Multiplicity results for an eigenvalue problem for hemivariational inequalities in strip-like domains. Set-Valued Anal. 13 (2005) 85-103
6. N. Nonlinear Anal. 67 (2007) 2232-2239
7. Zhang G., Zhang W., and Liu S. Multiplicity result for a discrete eigenvalue problem with discontinuous nonlinearities. J. Math. Anal. Appl. 328 (2007) 1068-1074
8. Ricceri B. Minimax theorems for limits of parametrized functions having at most one local minimum lying in a certain set. Topology Appl. 153 (2006) 3308-3312
9. Faraci F., Iannizzotto A., Kupán P., and Varga Cs. Existence and multiplicity results for hemivariational inequalities with two parameters. Nonlinear Anal. 67 (2007) 2654-2669
10. A. Kristály, W. Marzantowicz, Cs. Varga, A non-smooth three critical points theorem with applications in differential inclusions, doi:10.1007/s10898-009-9408-0
11. Motreanu D., and Panagiotopoulos P.D. Minimax Theorems and Qualitative Properties of the Solutions of Hemivariational Inequalities (1999), Kluwer Academic Publishers
12. Ioffe A.D., and Levin V.L. Subdifferentials of convex functions. Trans. Moscow Math. Soc. 26 (1972) 1-72
13. Clarke F.H. Optimization and Nonsmooth Analysis (1983), John Wiley & Sons
14. Panagiotopoulos P.D. Inequality Problems in Mechanics and Applications. Convex and Nonconvex Energy Functions (1985), Birkhäuser
15. Kinderlehrer D., and Stampacchia G. An Introduction to Variational Inequalities and their Applications (1980), Academic Press
16. Chang K.C. Variational methods for nondifferentiable functionals and their applications to partial differential equations. J. Math. Anal. Appl. 80 (1981) 102-129
17. Kyritsi S.Th., and Papageorgiou N.S. Nonsmooth critical point theory on closed convex sets and nonlinear hemivariational inequalities. Nonlinear Anal. 61 (2005) 373-403
18. Kyritsi S.Th., and Papageorgiou N.S. An obstacle problem for nonlinear hemivariational inequalities at resonance. J. Math. Anal. Appl. 276 (2002) 292-313
19. Szulkin A. Minimax principles for lower semicontinuous functions and applications to nonlinear boundary value problems. Ann. Inst. H. Poincaré Anal. Non Linéaire 3 (1986) 77-109
20. Livrea R., and Marano S.A. Existence and classification of critical points for nondifferentiable functions. Adv. Differential Equations 9 (2004) 961-978
21. Struwe M. Variational Methods. Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems (2000), Springer-Verlag
22. Sion M. On general minimax theorems. Pacific J. Math. 8 (1958) 171-176
23. Gasiński L., and Papageorgiou N.S. Nonlinear Analysis (2006), Chapman & Hall/CRC
24. Anello G. A multiplicity theorem for critical points of functionals on reflexive Banach spaces. Arch. Math. (Basel) 82 (2004) 172-179
25. Iannizzotto A., and Papageorgiou N.S. Existence of three nontrivial solutions for nonlinear Neumann hemivariational inequalities. Nonlinear Anal. 70 (2009) 3285-3297
26. Goeleven D., Motreanu D., and Panagiotopoulos P.D. Eigenvalue problems for variational-hemivariational inequalities at resonance. Nonlinear Anal. 33 (1998) 161-180
27. Szulkin A. Positive solutions of variational inequalities: A degree theoretic approach. J. Differential Equations 57 (1985) 90-111
28. Adams R.A. Sobolev Spaces (1975), Academic Press
29. Chabrowski J. Variational Methods for Potential Operator Equations (1997), de Gruyter
30. Ladyzhenskaya O.A., and Ural'tseva N.N. Linear and Quasilinear Elliptic Equations (1968), Academic Press
31. Brézis H., and Stampacchia G. Sur la régularité de la solution d'inéquations elliptiques. Bull. Soc. Math. France 96 (1968) 153-180
32. Le V.K., and Schmitt K. Minimization problems for noncoercive functionals subject to constraints. Trans. Amer. Math. Soc. 347 (1995) 4485-4513
33. Bonanno G. A minimax inequality and its applications to ordinary differential equations. J. Math. Anal. Appl. 270 (2002) 210-229