Existence of a periodic solution for superlinear second order ODEs

Abstract

We prove a necessary and sufficient condition for the existence of a T-periodic solution for the time-periodic second order differential equation x¨+f(t,x)+p(t,x,x˙)=0, where f grows superlinearly in x uniformly in time, while p is bounded. Our method is based on a fixed-point theorem which uses the rotational properties of the dynamics.