Abstract and Applied Analysis
Volume 7 (2002), Issue 5, Pages 259-277
Existence theorems for elliptic hemivariational inequalities involving the -Laplacian
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 -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.