On Differential Equations with Delay in Banach Spaces and Attractors for Retarded Lattice Dynamical Systems

Abstract

In this paper we first prove a rather general theorem about existence of solutions for an abstract differential equation in a Banach space by assuming that the nonlinear term is in some sense weakly continuous. We then apply this result to a lattice dynamical system with delay, proving also the existence of a global compact attractor for such system.