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

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  • 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).

Suggested Citation

  • Francesca Papalini, 2007. "Nonlinear Periodic Systems with the p‐Laplacian: Existence and Multiplicity Results," Abstract and Applied Analysis, John Wiley & Sons, vol. 2007(1).
    • Handle: RePEc:wly:jnlaaa:v:2007:y:2007:i:1:n:080394
    DOI: 10.1155/2007/80394
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    References listed on IDEAS

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    1. Zdzisław Denkowski & Stanisław Migórski & Nikolas S. Papageorgiou, 2003. "An Introduction to Nonlinear Analysis: Theory," Springer Books, Springer, number 978-1-4419-9158-4, October.
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