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

Pages: 1401 - 1414, Volume 10, Issue 5, September 2011

doi:10.3934/cpaa.2011.10.1401       Abstract        References        Full Text (364.1K)       Related Articles

D. Motreanu - Département de Mathématiques, Université de Perpignan, Avenue de Villeneuve 52, 66860 Perpignan Cedex, France (email)
V. V. Motreanu - Ben Gurion University of the Negev, Department of Mathematics, Be'er Sheva 84105, Israel (email)
Nikolaos S. Papageorgiou - Department of Mathematics, National Technical University, Zografou Campus, Athens 15780, Greece (email)

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.

Keywords:  Resonant system, indefinite linear part, reduction method, coercive functional, local linking, $C$-condition.
Mathematics Subject Classification:  Primary: 34C25; Secondary: 49J40.

Received: March 2009;      Revised: August 2010;      Published: April 2011.

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