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1. CMB 2007 (vol 50 pp. 356)

Filippakis, Michael E.; Papageorgiou, Nikolaos S.
Existence of Positive Solutions for Nonlinear Noncoercive Hemivariational Inequalities
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
Categories:35J20, 35J60, 35J85

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