Global asymptotic behavior of solutions of a forced delay difference equation

Abstract

In this paper, we consider the nonautonomous forced delay difference equation Δx n = p nf(x n − k) + r n, n = 0,1,2,…, where the forcing term { r n } is a sequence of real numbers, { p n } a sequence of positive real numbers, k a nonnegative integer. We obtain new sufficient conditions so that every solution of the equation converges to zero. When we apply our results to some well-known delay difference population models, the corollaries improve some recent results.