Abstract and Applied Analysis
Volume 2007 (2007), Article ID 80394, 23 pages
Nonlinear Periodic Systems with the -Laplacian: Existence and Multiplicity Results
Department of Mathematical Sciences, Polytechnic University of Marche, Via Brecce Bianche, Ancona 60131, Italy
Received 2 March 2007; Accepted 20 April 2007
Academic Editor: Nikolaos S. Papageorgiou
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.
We study second-order nonlinear periodic systems driven by the vector -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).