Solutions and multiple solutions for problems with the p - Laplacian

• Autores: L.-S. Hu, Nikolaos S. Papageorgiou
• Localización: Monatshefte für mathematik, ISSN 0026-9255, Vol. 150, Nº 4, 2007, págs. 309-326
• Idioma: inglés
• DOI: 10.1007/s00605-006-0432-6
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• Resumen

  • 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 ? < ?2 = 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.