Shadowing for nonautonomous difference equations with infinite delay

We formulate sufficient conditions under which a large class of semilinear nonautonomous difference equations with infinite delay is Hyers-Ulam stable. These conditions require that the nonautonomous linear part admits an exponential dichotomy and the nonlinear perturbations are uniformly Lipschitz continuous with a sufficiently small Lipschitz constant. In the more general case when the linear part admits a shifted exponential dichotomy, we are able to provide sufficient conditions for the existence of a certain weighted form of the shadowing property. (c) 2021 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).