Nonlinear Periodic Systems with the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>p</mml:mi></mml:math>-Laplacian: Existence and Multiplicity Results

Papalini, Francesca

doi:https://doi.org/10.1155/2007/80394

Abstract and Applied Analysis

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Research Article | Open Access

Volume 2007 | Article ID 080394 | https://doi.org/10.1155/2007/80394

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

Francesca Papalini¹

Academic Editor: Nikolaos S. Papageorgiou

Received02 Mar 2007

Accepted20 Apr 2007

Published31 May 2007

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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Copyright

Copyright © 2007 Francesca Papalini. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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