location:  Publications → journals → CMB
Abstract view

# Existence of Positive Solutions for Nonlinear Noncoercive Hemivariational Inequalities

Published:2007-09-01
Printed: Sep 2007
• Michael E. Filippakis
• Nikolaos S. Papageorgiou
 Format: HTML LaTeX MathJax PDF PostScript

## 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)

 top of page | contact us | privacy | site map |