Asymptotic properties of solutions to nonautonomous Volterra difference systems with infinite delay

Abstract

We show that under certain conditions there is a one-to-one correspondence between weighted bounded solutions of a linear nonautonomous Volterra difference system with infinite delay and its perturbed system. Under additional assumptions, this correspondence is elevated to asymptotic equivalence. On the other side, we prove the existence of weighted convergent solutions. © 2001 Elsevier Science Ltd.