Multiple Solutions of Eigenvalue Problems for Hemivariational Inequalities

1999 ◽  
pp. 133-168
Author(s):  
D. Motreanu ◽  
P. D. Panagiotopoulos
Keyword(s):  
Multiple Solutions ◽  
Eigenvalue Problems ◽  
Hemivariational Inequalities

Multiple solutions for a class of eigenvalue problems in hemivariational inequalities

1997 ◽  
Vol 29 (1) ◽  
pp. 9-26 ◽  
Author(s):  
D. Goeleven ◽  
D. Motreanu ◽  
P.D. Panagiotopoulos
Keyword(s):  
Multiple Solutions ◽  
Eigenvalue Problems ◽  
Hemivariational Inequalities

scholarly journals ON EIGENVALUE PROBLEMS FOR ELLIPTIC HEMIVARIATIONAL INEQUALITIES

2008 ◽  
Vol 51 (2) ◽  
pp. 407-419 ◽  
Author(s):  
Zhenhai Liu ◽  
Guifang Liu
Keyword(s):  
Dirichlet Problem ◽  
Eigenvalue Problems ◽  
Hemivariational Inequalities ◽  
Generalized Gradient ◽  
At Resonance ◽  
Quasilinear Elliptic ◽  
First Eigenfunction

AbstractThis paper is devoted to the Dirichlet problem for quasilinear elliptic hemivariational inequalities at resonance as well as at non-resonance. Using Clarke's notion of the generalized gradient and the property of the first eigenfunction, we also build a Landesman–Lazer theory in the non-smooth framework of quasilinear elliptic hemivariational inequalities.

Hemivariational Inequalities: Eigenvalue Problems

2008 ◽  
pp. 1483-1488
Author(s):  
Daniel Goeleven ◽  
Dumitru Motreanu
Keyword(s):  
Eigenvalue Problems ◽  
Hemivariational Inequalities

Multiple Solutions for Resonant Hemivariational Inequalities via Minimax Methods

2009 ◽  
Vol 9 (3) ◽  
Author(s):  
Sophia Th. Kyritsi ◽  
Donal O’ Regan ◽  
Nikolaos S. Papageorgiou
Keyword(s):  
Multiple Solutions ◽  
Principal Eigenvalue ◽  
Point Theory ◽  
Hemivariational Inequalities ◽  
Dirichlet Problems ◽  
Nonsmooth Critical Point Theory ◽  
Minimax Methods ◽  
Nonsmooth Critical Point ◽  
Multiplicity Theorem ◽  
The Right

AbstractIn this paper we consider nonlinear Dirichlet problems driven by the p-Laplacian differential operator with a nonsmooth potential (hemivariational inequalities). We assume that the problem is resonant at infinity with respect to λ1 > 0 (the principal eigenvalue of the Dirichlet p-Lapalcian) from the right. Using minimax methods based on the nonsmooth critical point theory we prove an existence and a multiplicity theorem.

Solutions and multiple solutions for quasilinear hemivariational inequalities at resonance

2001 ◽  
Vol 131 (5) ◽  
pp. 1091-1111 ◽  
Author(s):  
Leszek Gasiński ◽  
Nikolaos S. Papageorgiou
Keyword(s):  
Variational Principle ◽  
Critical Point Theory ◽  
Multiple Solutions ◽  
Existence Theorems ◽  
Point Theory ◽  
Hemivariational Inequalities ◽  
Locally Lipschitz Functions ◽  
Strong Resonance ◽  
At Resonance ◽  
Locally Lipschitz

In this paper we consider quasilinear hemivariational inequalities at resonance. We obtain existence theorems using Landesman-Lazer-type conditions and multiplicity theorems for problems with strong resonance at infinity. Our method of proof is based on the non-smooth critical point theory for locally Lipschitz functions and on a generalized version of the Ekeland variational principle.

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