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Existence of Positive Solutions for Nonlinear Noncoercive Hemivariational Inequalities

Published online by Cambridge University Press:  20 November 2018

Michael E. Filippakis  and
Nikolaos S. Papageorgiou
Michael E. Filippakis
Affiliation:
Department of Mathematics, National Technical University, Zografou Campus, Athens 15780, Greece e-mail: mfilip@math.ntua.grnpapg@math.ntua.gr
Nikolaos S. Papageorgiou
Affiliation:
Department of Mathematics, National Technical University, Zografou Campus, Athens 15780, Greece e-mail: mfilip@math.ntua.grnpapg@math.ntua.gr
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Abstract

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In this paper we investigate the existence of positive solutions for nonlinear elliptic problems driven by the $p$-Laplacian with a nonsmooth potential (hemivariational inequality). Under asymptotic conditions that make the Euler functional indefinite and incorporate in our framework the asymptotically linear problems, using a variational approach based on nonsmooth critical point theory, we obtain positive smooth solutions. Our analysis also leads naturally to multiplicity results.

Keywords

35J2035J6035J85p-Laplacianlocally Lipschitz potentialnonsmooth critical point theoryprincipal eigenvaluepositive solutionsnonsmooth Mountain Pass Theorem
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 50 , Issue 3 , 01 September 2007 , pp. 356 - 364
Copyright
Copyright © Canadian Mathematical Society 2007

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