Mathematical Institute of the Serbian Academy of Science, Knez Mihailova 35/I, Beograd 11000 , 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 asymptotic periodicity of positive
solutions of the following difference equation:
, , where
are natural numbers such that , and , the function
increasing in the first arguments and decreasing in other
arguments, there is a decreasing function such that ,
, , , and . It is proved that if all
are even and all
are odd, every positive solution of the equation converges to
(not necessarily prime) a periodic solution of period two,
otherwise, every positive solution of the equation converges to a
unique positive equilibrium.