ASYMPTOTIC STABILITY OF INFINITE-DIMENSIONAL NONAUTONOMOUS DYNAMICAL SYSTEMS

Abstract

This paper is dedicated to the study of the problem of asymptotic stabil- ity for general non-autonomous dynamical systems (both with continuous and discrete time). We study the relation between diÆerent types of attractions and asymptotic stability in the framework of general non-autonomous dynamical systems. Specially we investigate the case of almost periodic systems, i.e., when the base (driving sys- tem) is almost periodic. We apply the obtained results we apply to diÆerent classes of non-autonomous evolution equations: Ordinary DiÆerential Equations, Functional DiÆerential Equations (both with Ønite retard and neutral type) and Semi-Linear Parabolic Equations