Solutions for nonlinear variational inequalities with a nonsmooth potential

Michael E. Filippakis and Nikolaos S. Papageorgiou

Abstract and Applied Analysis, 2004, vol. 2004, 1-15

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 φ = φ 1 + φ 2 with φ 1 locally Lipschitz and φ 2 proper, convex, lower semicontinuous.

Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:318012

DOI: 10.1155/S1085337504312017

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