Copyright © 2009 Hongjian Xi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We study the boundedness of the
difference equation , where and the initial values . We show that the solution
of this equation converges to
if or for all
; otherwise is unbounded. Besides, we obtain the set of all initial values such that the positive solutions
of this equation are bounded, which
answers the open problem 6.10.12 proposed by Kulenović and Ladas (2002).