ON THE ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF LINEAR DEGENERATE DIFFERENCE EQUATIONS

Abstract

The asymptotic properties of solutions of the linear degenerate discrete equations Bxn+1 = Axn (∗) on a Banach space are considered, where A and B are closed unbounded linear operators from a Banach space X to a Banach space Y . Using a construction of a subspace L of exponentially bounded solutions, an operator T on L such that xn satisfies Eq.(*) on L if and only if xn = Tnx0, and using results on almost periodicity of discrete semigroups of operators {Tn : n ≥ 0}, we obtain criteria for asymptotic almost periodicity of solutions of Eq.(*).