Solutions and multiple solutions for problems with the p-Laplacian

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.

Department(s)

Mathematics

Document Type

Article

DOI

https://doi.org/10.1007/s00605-006-0432-6

Keywords

First and second eigenvalues of the p-Laplacian, Linking sets, Local linking condition, Locally Lipschitz potential, Nonsmooth C and PS-conditions

Publication Date

4-1-2007

Journal Title

Monatshefte fur Mathematik

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