On the Existence of Positive Solutions for Hemivariational Inequalities Driven by the p-Laplacian期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

On the Existence of Positive Solutions for Hemivariational Inequalities Driven by the p-Laplacian

Authors:	Michael?Filippakis,Leszek?Gasiński,Nikolaos?S.?Papageorgiou mailto:npapg@math.ntua.gr" title=" npapg@math.ntua.gr" itemprop=" email" data-track=" click" data-track-action=" Email author" data-track-label=" " >Email author

Affiliation:	(1) Department of Mathematics, National Technical University, Zografou Campus, Athens, 15780, Greece;(2) Institute of Computer Science, Jagiellonian University, ul. Nawojki 11, 30072 Cracow, Poland

Abstract:	We study nonlinear elliptic problems driven by the p-Laplacian and with a nonsmooth locally Lipschitz potential (hemivariational inequality). We do not assume that the nonsmooth potential satisfies the Ambrosetti--Rabinowitz condition. Using a variational approach based on the nonsmooth critical point theory, we establish the existence of at least one smooth positive solution.Mathematics Subject Classifications (2000). 35J50, 35J85, 35R70.This article is Revised version.Leszek Gasiski is an award holder of the NATO Science FellowshipProgramme, which was spent in the National Technical University of Athens.

Keywords:	Clarke subdifferential hemivariational inequality nonsmooth critical point theory nonsmooth Cerami condition nonsmooth Mountain Pass Theorem p-Laplacian positive solution principal eigenvalue and eigenfunction.
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