Robustness of exponential dichotomy in a class of generalised almost periodic linear differential equations in infinite dimensional Banach spaces

Abstract

In this paper we study the robustness of the exponential dichotomy in nonautonomous linear ordinary differential equations under integrally small perturbations in infinite dimensional Banach spaces. Some applications are ob- tained to the case of rapidly oscillating perturbations, with arbitrarily small periods, showing that even in this case the stability is robust. These results extend to infinite dimensions some results given in Coppel [2]. Based in Ro- drigues [6] and in Kloeden & Rodrigues [5,7] we use the class of functions that we call Generalized Almost Periodic Functions that extend the usual class of almost periodic functions and are suitable to model these oscillating per- turbations. We also present an infinite dimensional example of the previous results.