Nonlinear hemivariational inequalities with eigenvalues near zero

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2005, 2005(Special): 317-326. doi: 10.3934/proc.2005.2005.317

Nonlinear hemivariational inequalities with eigenvalues near zero

Leszek Gasiński ^1, and Nikolaos S. Papageorgiou ^2,

1.	Jagiellonian University, Institute of Computer Science, ul. Nawojki 11, 30072 Kraków, Poland
2.	Department of Mathematics, National Technical University, Zografou Campus, Athens 15780

Received September 2004 Revised March 2005 Published September 2005

Abstract
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In this paper we consider an eigenvalue problem for a quasilinear hemivariational inequality of the type $-\Delta_p x(z) -\lambda f(z,x(z))\in \partial j(z,x(z))$ with null boundary condition, where $f$ and $j$ satisfy ``$p-1$-growth condition''. We prove the existence of a nontrivial solution for $\lambda$ sufficiently close to zero. Our approach is variational and is based on the critical point theory for nonsmooth, locally Lipschitz functionals due to Chang [4].

Keywords: p-Laplacian, Palais-Smale condition, Hemivariational inequality, eigenvalue problem, critical point theory, Clarke subdi®erential, mountain pass theorem..

Mathematics Subject Classification: Primary: 35J60; Secondary: 49J4.

Citation: Leszek Gasiński, Nikolaos S. Papageorgiou. Nonlinear hemivariational inequalities with eigenvalues near zero. Conference Publications, 2005, 2005 (Special) : 317-326. doi: 10.3934/proc.2005.2005.317

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