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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

D. Motreanu 1, , V. V. Motreanu 2, and  Nikolaos S. Papageorgiou 3,

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.
Keywords: Second order periodic system, PS-condition, multiple solutions, local linking., nonsmooth reduction method.
Mathematics Subject Classification: Primary: 34C25; Secondary: 49J4.
Citation: D. Motreanu, V. V. Motreanu, Nikolaos S. Papageorgiou. Two nontrivial solutions for periodic systems with indefinite linear part. Discrete and Continuous Dynamical Systems, 2007, 19 (1) : 197-210. doi: 10.3934/dcds.2007.19.197
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