On a nonautonomous difference equation with bounded coefficient

In this paper we investigate the boundedness, the persistence and the attractivity of the positive solutions of the nonautonomous difference equation xn+1 = pn + xn−k k−1 j=0 1 xn−j , where k is a positive integer, pn is a positive bounded sequence and the initial values are positive real numbers. © 2006 Elsevier Inc. All rights reserved.