## Abstract and Applied Analysis

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

Francesca Papalini

#### 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).

#### Article information

Source
Abstr. Appl. Anal., Volume 2007 (2007), Article ID 80394, 23 pages.

Dates
First available in Project Euclid: 5 July 2007

https://projecteuclid.org/euclid.aaa/1183666877

Digital Object Identifier
doi:10.1155/2007/80394

Mathematical Reviews number (MathSciNet)
MR2320799

Zentralblatt MATH identifier
1156.34011

#### Citation

Papalini, Francesca. Nonlinear Periodic Systems with the $p$ -Laplacian: Existence and Multiplicity Results. Abstr. Appl. Anal. 2007 (2007), Article ID 80394, 23 pages. doi:10.1155/2007/80394. https://projecteuclid.org/euclid.aaa/1183666877

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