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multiple periodic solutions

Proceedings of the Edinburgh Mathematical Society (1)

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A MULTIPLICITY THEOREM FOR A PERTURBED SECOND-ORDER NON-AUTONOMOUS SYSTEM
Francesca Faraci, Antonio Iannizzotto
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 49 / Issue 2 / June 2006

Published online by Cambridge University Press:

30 May 2006, pp. 267-275
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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.