Abstract and Applied Analysis 
Volume 7 (2002), Issue 5, Pages 259-277
doi:10.1155/S1085337502000908

Existence theorems for elliptic hemivariational inequalities involving the p-Laplacian

Nikolaos C. Kourogenis and Nikolaos S. Papageorgiou

 Department of Applied Mathematics and Physics, National Technical University, Zografou Campus, Athens 157 80, Greece
Received 25 April 2001

Abstract

We study quasilinear hemivariational inequalities involving the p-Laplacian. We prove two existence theorems. In the first, we allow “crossing” of the principal eigenvalue by the generalized potential, while in the second, we incorporate problems at resonance. Our approach is based on the nonsmooth critical point theory for locally Lipschitz energy functionals.