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ON THE EXISTENCE OF MULTIPLE PERIODIC SOLUTIONS FOR EQUATIONS DRIVEN BY THE $p$-LAPLACIAN AND WITH A NON-SMOOTH POTENTIAL

Published online by Cambridge University Press:  27 January 2003

Leszek Gasiński  and
Nikolaos S. Papageorgiou
Leszek Gasiński
Affiliation:
Jagiellonian University, Institute of Computer Science, ul. Nawojki 11, 30072 Cracow, Poland
Nikolaos S. Papageorgiou
Affiliation:
National Technical University, Department of Mathematics, Zografou Campus, Athens 15780, Greece ([email protected])
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Abstract

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In this paper we examine periodic problems driven by the scalar $p$-Laplacian. Using non-smooth critical-point theory and a recent multiplicity result based on local linking (the original smooth version is due to Brezis and Nirenberg), we prove three multiplicity results, the third for semilinear problems with resonance at zero. We also study a quasilinear periodic eigenvalue problem with the parameter near resonance. We prove the existence of three distinct solutions, extending in this way a semilinear and smooth result of Mawhin and Schmitt.

AMS 2000 Mathematics subject classification: Primary 34C25

Keywords

non-smooth critical-point theorylocally Lipschitz functionalClarke subdifferentialnon-smooth Palais–Smale conditionlocal linkingcoercive functional
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 46 , Issue 1 , February 2003 , pp. 229 - 249
Copyright
Copyright © Edinburgh Mathematical Society 2003