Nonlinear Periodic Systems with the p -Laplacian: Existence and Multiplicity Results



Abstract and Applied Analysis

Nonlinear Periodic Systems with the $p$-Laplacian: Existence and Multiplicity Results

Francesca Papalini

Source: Abstr. Appl. Anal. Volume 2007 (2007), 23 pages.

Abstract

We study second-order nonlinear periodic systems driven by the vector $p$-Laplacian with a nonsmooth, locally Lipschitz potential function. Under minimal and natural hypotheses on the potential and using variational methods based on the nonsmooth critical point theory, we prove existence theorems and a multiplicity result. We conclude the paper with an existence theorem for the scalar problem, in which the energy functional is indefinite (unbounded from both above and below).

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.aaa/1183666877
Digital Object Identifier: doi:10.1155/2007/80394
Mathematical Reviews number (MathSciNet): MR2320799


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