Solutions and multiple solutions for problems with the p-Laplacian |
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Authors: | Shouchuan Hu Nikolaos S. Papageorgiou |
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Affiliation: | (1) Southwest Missouri State University, Springfield, MO, USA;(2) National Technical University, Athens, Greece |
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Abstract: | In this paper we consider two nonlinear elliptic problems driven by the p-Laplacian and having a nonsmooth potential (hemivariational inequalities). The first is an eigenvalue problem and we prove that if the parameter λ < λ2 = the second eigenvalue of the p-Laplacian, then there exists a nontrivial smooth solution. The second problem is resonant both near zero and near infinity for the principal eigenvalue of the p-Laplacian. For this problem we prove a multiplicity result. Our approach is variational based on the nonsmooth critical point theory. Second author is Corresponding author. |
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Keywords: | 2000 Mathematics Subject Classification: 35J20 35J85 |
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