Periodic Solutions For ẋ = Ax + G(x, t) + ∊p(t)

Abstract

We wish to establish the existence of a periodic solution to1where x, g and p are n-vectors, A is an n × n constant matrix, and ∊ is a small scalar parameter. We assume that g and p are locally Lipschitz in x and continuous and T-periodic in t, and that the origin is a point of asymptotically stable equilibrium, when ∊ = 0.