Almost periodic solutions for a class of Duffing-like systems

Abstract

We prove the existence of infinitely many limit periodic solutions for Duffing-like systems of the type $-\ddot{q} = g(t,q)$, where $g$ is limit periodic in time and has a non-degenerate homoclinic solution to the hyperbolic stationary solution $q \equiv 0$. Moreover, we can deal with almost periodic perturbations of the above class of systems. In this case we prove the existence of almost periodic solutions and we show that these solutions are quasi-periodic whenever the perturbation is quasi periodic.