Nonautonomous resonant periodic systems with
indefinite linear part and a nonsmooth potential
D. Motreanu - Département de Mathématiques, Université de Perpignan, Avenue de Villeneuve 52, 66860 Perpignan Cedex, France (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,
Received: March 2009; Revised: August 2010; Published: April 2011.
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