Dynamics of non-autonomous first order lattice systems in weighted spaces

Abstract

In a weighted Hilbert space, the existence of a uniform global attractor for a family of first order non-autonomous deterministic lattice dynamical systems with a nonlinear part of the form ft,u=fit,ui−m,…,ui+mi∈Z is carefully investigated, where ft,⋅ is an element of the hull of an almost periodic function in a suitable Banach space.