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

Michael Filippakis, Leszek Gasiński and Nikolaos Papageorgiou ()

Journal of Global Optimization, 2005, vol. 31, issue 1, 173-189

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. Copyright Springer Science+Business Media New York 2005

Keywords: Clarke subdifferential; hemivariational inequality; nonsmooth critical point theory; nonsmooth Cerami condition; nonsmooth Mountain Pass Theorem; p-Laplacian; positive solution; principal eigenvalue and eigenfunction. (search for similar items in EconPapers)
Date: 2005
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DOI: 10.1007/s10898-003-5444-3

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