Nonautonomous resonant periodic systems withindefinite linear part and a nonsmooth potential

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

doi:10.3934/cpaa.2011.10.1401

Article Contents

2011, Volume 10, Issue 5: 1401-1414. Doi: 10.3934/cpaa.2011.10.1401

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Nonautonomous resonant periodic systems with indefinite linear part and a nonsmooth potential

1.
Département de Mathématiques, Université de Perpignan, Avenue de Villeneuve 52, 66860 Perpignan Cedex
2.
Ben Gurion University of the Negev, Department of Mathematics, Be'er Sheva 84105
3.
Department of Mathematics, National Technical University, Zografou Campus, Athens 15780

Received: March 2009

Revised: August 2010

Published: September 2011

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Abstract

A nonautonomous second order system with a nonsmooth potential is studied. It is assumed that the system is asymptotically linear at infinity and resonant (both at infinity and at the origin), with respect to the zero eigenvalue. Also, it is assumed that the linearization of the system is indefinite. Using a nonsmooth variant of the reduction method and the local linking theorem, we show that the system has at least two nontrivial solutions.

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

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