The perturbation of almost periodic solution of almost periodic system (Q1077611)

This paper uses the exponential dichotomy and the method of averaging to establish that under certain conditions on the functions f and g, the almost periodic differential system \(dx/dt=f(x,t)+\epsilon^ 2g(x,t,\epsilon)\) for \(\epsilon >0\) sufficiently small has an almost periodic solution x(t,\(\epsilon)\) when the unperturbed system with \(\epsilon =0\) has an almost periodic solution \(x_ 0(t)\). Furthermore, \(\lim_{\epsilon \to 0}x(t,\epsilon)=x_ 0(t)\) uniformly for all t.