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

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作者
Michael Filippakis
Leszek Gasiński
Nikolaos S. Papageorgiou
机构
[1] National Technical University,Department of Mathematics
[2] Jagiellonian University,Institute of Computer Science
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关键词
Clarke subdifferential; hemivariational inequality; nonsmooth critical point theory; nonsmooth Cerami condition; nonsmooth Mountain Pass Theorem; p-Laplacian; positive solution; principal eigenvalue and eigenfunction.;
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摘要
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.
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页码:173 / 189
页数:16
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