Remarks on dynamical systems with weak forces

We study the existence of T-periodic solutions for the forced system of differential equations –ÿ=V(y)+h(t), where h is T-periodic and V is defined in an open, bounded and convex subset of R^N and V– as y tends to the boundary of the set. We prove existence of at least one solution only requiring convexity of V near the boundary.Supported by Ministero Pubblica Istruzione, Gruppo Nazionale (40%) Calcolo delle Variazioni