Abstract and Applied Analysis
Volume 2004 (2004), Issue 8, Pages 635-649

Solutions for nonlinear variational inequalities with a nonsmooth potential

Michael E. Filippakis and Nikolaos S. Papageorgiou

Department of Mathematics, National Technical University of Athens, Zografou Campus, Athens 15780, Greece

Received 4 November 2003

Copyright © 2004 Michael E. Filippakis 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.


First we examine a resonant variational inequality driven by the p-Laplacian and with a nonsmooth potential. We prove the existence of a nontrivial solution. Then we use this existence theorem to obtain nontrivial positive solutions for a class of resonant elliptic equations involving the p-Laplacian and a nonsmooth potential. Our approach is variational based on the nonsmooth critical point theory for functionals of the form φ=φ1+φ2 with φ1 locally Lipschitz and φ2 proper, convex, lower semicontinuous.