## Abstract and Applied Analysis

### Solutions for nonlinear variational inequalities with a nonsmooth potential

#### Abstract

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 $\varphi=\varphi_1+\varphi_2$ with $\varphi_1$ locally Lipschitz and $\varphi_2$ proper, convex, lower semicontinuous.

#### Article information

Source
Abstr. Appl. Anal., Volume 2004, Number 8 (2004), 635-649.

Dates
First available in Project Euclid: 20 September 2004

https://projecteuclid.org/euclid.aaa/1095684285

Digital Object Identifier
doi:10.1155/S1085337504312017

Mathematical Reviews number (MathSciNet)
MR2096944

Zentralblatt MATH identifier
1133.35375

Subjects
Primary: 35J85 35J20

#### Citation

Filippakis, Michael E.; Papageorgiou, Nikolaos S. Solutions for nonlinear variational inequalities with a nonsmooth potential. Abstr. Appl. Anal. 2004 (2004), no. 8, 635--649. doi:10.1155/S1085337504312017. https://projecteuclid.org/euclid.aaa/1095684285