Advances in Difference Equations
Volume 2009 (2009), Article ID 394635, 9 pages
doi:10.1155/2009/394635

On a conjecture for a higher-order rational difference equation

Abstract

This paper studies the global asymptotic stability for positive solutions to the higher order rational difference equation xn=(∏j=1m(xn−kj+1)+∏j=1m(xn−kj−1))/(∏j=1m(xn−kj+1)−∏j=1m(xn−kj−1)), n=0,1,2,…, where m is odd and x−km,x−km+1,…,x−1∈(0,∞). Our main result generalizes several others in the recent literature and confirms a conjecture by Berenhaut et al., 2007.