Periodic solutions for a class of singularly perturbed systems

In this paper we provide conditions to ensure the existence, for epsilon > 0 sufficiently small, of periodic solutions of given period T > 0 for a class of singularly perturbed first order differential systems. Here epsilon > 0 is the perturbation parameter. Our approach, based on the topological degree theory and the averaging theory, permits to weaken the conditions in ([5], Theorem 2) under which the existence of periodic solutions is proved