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

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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.

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Authors and Affiliations

  1. Department of Mathematics, National Technical University, Zografou Campus, Athens, 15780, Greece

    Michael Filippakis & Nikolaos S. Papageorgiou

  2. Institute of Computer Science, Jagiellonian University, ul. Nawojki 11, 30072, Cracow, Poland

    Leszek Gasiński

Authors
  1. Michael Filippakis
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  2. Leszek Gasiński
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  3. Nikolaos S. Papageorgiou
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Corresponding author

Correspondence to Nikolaos S. Papageorgiou.

Additional information

Mathematics Subject Classifications (2000). 35J50, 35J85, 35R70.

This article is Revised version.

Leszek Gasiński is an award holder of the NATO Science FellowshipProgramme, which was spent in the National Technical University of Athens.

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Filippakis, M., Gasiński, L. & Papageorgiou, N.S. On the Existence of Positive Solutions for Hemivariational Inequalities Driven by the p-Laplacian. J Glob Optim 31, 173–189 (2005). https://doi.org/10.1007/s10898-003-5444-3

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  • DOI: https://doi.org/10.1007/s10898-003-5444-3

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