Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, Harris Hall, 1015 Floyd Avenue, P.O. Box 842014, Richmond, VA 23284-2014, USA
Academic Editor: Martin J. Bohner
Copyright © 2009 D. M. Chan 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 investigate the global behavior of the second-order difference equation , where initial conditions and all coefficients are positive. We find conditions
on under which the even and odd subsequences of a
positive solution converge, one to zero and the other to a nonnegative
number; as well as conditions where one of the subsequences diverges
to infinity and the other either converges to a positive number or diverges
to infinity. We also find initial conditions where the solution
monotonically converges to zero and where it diverges to infinity.