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Positive solutions and multiple solutions for periodic problems driven by scalar p -Laplacian

✍ Scribed by Shouchuan Hu; N. S. Papageorgiou

Publisher
John Wiley and Sons
Year
2006
Tongue
English
Weight
195 KB
Volume
279
Category
Article
ISSN
0025-584X

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✦ Synopsis

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. (Β© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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