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.
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Hu, S., Papageorgiou, N. Solutions and multiple solutions for problems with the p-Laplacian. Mh Math 150, 309–326 (2007). https://doi.org/10.1007/s00605-006-0432-6
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DOI: https://doi.org/10.1007/s00605-006-0432-6