Two nontrivial solutions for periodic systems with indefinite linear part

D. Motreanu; V. V. Motreanu; Nikolaos S. Papageorgiou

doi:10.3934/dcds.2007.19.197

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2007, Volume 19, Issue 1: 197-210. Doi: 10.3934/dcds.2007.19.197

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Two nontrivial solutions for periodic systems with indefinite linear part

1.
Département de Mathématiques, Université de Perpignan, Avenue de Villeneuve 52, 66860 Perpignan Cedex
2.
Université de Perpignan, Département de Mathématiques, 52, Avenue Paul Alduy, 66860 Perpignan
3.
Department of Mathematics, National Technical University, Zografou Campus, Athens 15780

Received: June 30, 2006

Revised: April 30, 2007

Published: December 2006

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Abstract

We consider second order periodic systems with a nonsmooth potential and an indefinite linear part. We impose conditions under which the nonsmooth Euler functional is unbounded. Then using a nonsmooth variant of the reduction method and the nonsmooth local linking theorem, we establish the existence of at least two nontrivial solutions.

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Mathematics Subject Classification: Primary: 34C25; Secondary: 49J40.

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