Abstract and Applied Analysis
Volume 7 (2002), Issue 5, Pages 259-277

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

Copyright © 2002 Nikolaos C. Kourogenis and Nikolaos S. Papageorgiou. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.