Global behavior of solutions of a nonlinear difference equation

摘要

Our aim in this paper is to investigate the persistence and the global attractivity of solutions of the equationxn+1=f(xn,xn−1,…,xn−k)forn=0,1,…,where f is a continuous, positive and decreasing function on [(0,∞)k+1,(0,∞)]. The results are applied to the difference equationyn+1=Aypn+1yqn−kforn=0,1,⋯,where A,p,q∈(0,∞),k∈{2,3,…}.