# American Institute of Mathematical Sciences

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

## Nonlinear hemivariational inequalities with eigenvalues near zero

 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

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].
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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