Existence of Eigenfunctions for Nonlinear Hemivariational Inequalities with Small Eigenvalues


       Leszek Gasiński, gasinski(at)softlab.ii.uj.edu.pl, http://www.ii.uj.edu.pl/~gasinski/
       Jagiellonian University, Institute of Computer Science, Nawojki 11, 30-072 Cracow, Poland

       Nikolaos S. Papageorgiou
       National Technical University, Department of Mathematics, Zografou Campus, Athens 15780, Greece

Pages: 15

Abstract: In this paper we consider an eigenvalue problem for a quasilinear hemivariational inequality of the type

with null boundary condition. We prove the existence of a nontrivial solution for  λ  sufficiently close to zero. Our approach is variational and is based on the critical point theory for nonsmooth, locally Lipschitz functionals due to Chang 

Keywords: p-Laplacian, variational methods, critical point, locally Lipschitz functional, subdifferential, Palais-Smale condition, mountain pass theorem

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