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Nonlinear hemivariational inequalities with eigenvalues near zero

Pages: 317 - 326, Issue Special, August 2005

 Abstract        Full Text (234.3K)              

Leszek Gasiński - Jagiellonian University, Institute of Computer Science, ul. Nawojki 11, 30072 Kraków, Poland (email)
Nikolaos S. Papageorgiou - Department of Mathematics, National Technical University, Zografou Campus, Athens 15780, Greece (email)

Abstract: 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:  Hemivariational inequality, eigenvalue problem, p-Laplacian, critical point theory, Clarke subdi®erential, Palais-Smale condition, mountain pass theorem.
Mathematics Subject Classification:  Primary: 35J60; Secondary: 49J40.

Received: September 2004;      Revised: March 2005;      Published: September 2005.