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A MULTIPLICITY THEOREM FOR A PERTURBED SECOND-ORDER NON-AUTONOMOUS SYSTEM

Published online by Cambridge University Press:  30 May 2006

Francesca Faraci  and
Antonio Iannizzotto
Francesca Faraci
Affiliation:
Department of Mathematics and Computer Science, University of Catania, Viale A. Doria 6, 95125 Catania, Italy (ffaraci@dmi.unict.it; iannizzotto@dmi.unict.it)
Antonio Iannizzotto
Affiliation:
Department of Mathematics and Computer Science, University of Catania, Viale A. Doria 6, 95125 Catania, Italy (ffaraci@dmi.unict.it; iannizzotto@dmi.unict.it)
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Abstract

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In this paper we establish a multiplicity result for a second-order non-autonomous system. Using a variational principle of Ricceri we prove that if the set of global minima of a certain function has at least $k$ connected components, then our problem has at least $k$ periodic solutions. Moreover, the existence of one more solution is investigated through a mountain-pass-like argument.

Keywords

Primary 34C2535A15multiple periodic solutionssecond-order non-autonomous systemcritical point theory
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 49 , Issue 2 , June 2006 , pp. 267 - 275
Copyright
Copyright © Edinburgh Mathematical Society 2006