Positive solutions and multiple solutions for periodic problems driven by scalarp -Laplacian

Abstract

In this paper we study a nonlinear second order periodic problem driven by a scalar p ‐Laplacian and with a nonsmooth, locally Lipschitz potential function. Using a variational approach based on the nonsmooth critical point theory for locally Lipschitz functions, we first prove the existence of nontrivial positive solutions and then establish the existence of a second distinct solution (multiplicity theorem) by strengthening further the hypotheses.

Department(s)

Mathematics

Document Type

Article

DOI

https://doi.org/10.1002/mana.200310423

Keywords

nonsmooth critical point theory, locally Lipschitz function, generalized subdifferential, nonsmooth PS ‐condition, Mountain Pass Theorem, positive solution, multiple solutions

Publication Date

8-9-2006

Journal Title

Mathematische Nachrichten

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