Mathematical Institute of the Serbian Academy of Sciences and Arts, Knez Mihailova 35/I, Belgrade 11001, Serbia
Copyright © 2007 Stevo Stević. 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 give a complete picture regarding the behavior of positive solutions of the following important difference equation:
, , where , and , are positive numbers such that and , and , are natural numbers such that
and . The case when is the most important. For the case we prove that if all , are even and all , are odd, then every positive solution of this equation converges to a periodic solution of period two, otherwise, every positive solution of the equation converges to a unique positive equilibrium.