Periodic solutions of dynamical systems

Abstract

In this paper we look for T-periodic solutions of dynamical systems. Particularly we consider the system $$ - \ddot x = \nabla U(x,t)$$ whereU ɛC 1(ℝ n x x ℝ, ℝ),U(x, t + T)=U(x,t) ∀ x ℝ n , ∀t ɛ ℝ T>0. We assume that the problem is asymptotically linear with a bounded nonlinearity. Under a resonance assumption, we find a multiplicity of T-periodic solutions for T large enough.