Discrete Dynamics in Nature and Society
Volume 2008 (2008), Article ID 917560, 8 pages
doi:10.1155/2008/917560

Existence of monotone solutions of a difference equation

Abstract

We consider the nonlinear difference equation xn+1=f(xn−k,xn−k+1,…,xn), n=0,1,…, where k∈{1,2,…} and the initial values x−k,x−k+1,…,x0∈(0,+∞). We give sufficient conditions under which this equation has monotone positive solutions which converge to the equilibrium, extending and including in this way some results of the literature.