Advances in Difference Equations
Volume 2009 (2009), Article ID 463169, 11 pages
doi:10.1155/2009/463169

On Boundedness of Solutions of the Difference Equation xn+1=(pxn+qxn1)/(1+xn) for q>1+p>1

Hongjian Xi , Taixiang Sun , Weiyong Yu and Jinfeng Zhao

Department of Mathematics, Guangxi University, Nanning, Guangxi 530004, China

Abstract

We study the boundedness of the difference equation xn+1=(pxn+qxn1)/(1+xn), n=0,1,, where q>1+p>1 and the initial values x1,x0(0,+). We show that the solution {xn}n=1 of this equation converges to x¯=q+p1 if xnx¯ or xnx¯ for all n1; otherwise {xn}n=1 is unbounded. Besides, we obtain the set of all initial values (x1,x0)(0,+)×(0,+) such that the positive solutions {xn}n=1 of this equation are bounded, which answers the open problem 6.10.12 proposed by Kulenović and Ladas (2002).