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March  2007, 19(1): 197-210. doi: 10.3934/dcds.2007.19.197

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, France 3 Department of Mathematics, National Technical University, Zografou Campus, Athens 15780

Received  July 2006 Revised  May 2007 Published  June 2007

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.
Citation: D. Motreanu, V. V. Motreanu, Nikolaos S. Papageorgiou. Two nontrivial solutions for periodic systems with indefinite linear part. Discrete & Continuous Dynamical Systems - A, 2007, 19 (1) : 197-210. doi: 10.3934/dcds.2007.19.197
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