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Existence of Positive Solutions for Nonlinear Noncoercive Hemivariational Inequalities |
Published:2007-09-01
Printed: Sep 2007
Printed: Sep 2007
- Michael E. Filippakis
- Nikolaos S. Papageorgiou
Abstract
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: | $p$-Laplacian, locally Lipschitz potential, nonsmooth critical point theory, principal eigenvalue, positive solutions, nonsmooth Mountain Pass Theorem |
| MSC Classifications: |
35J20 - Variational methods for second-order elliptic equations 35J60 - Nonlinear elliptic equations 35J85 - Unilateral problems and variational inequalities for elliptic PDE (See also 35R35, 49J40) |