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 present some methods for finding asymptotics of some classes of nonlinear higher-order difference equations. Among others, we confirm a conjecture posed by S. Stević (2005). Monotonous solutions of the equation
, , where , , , are natural numbers such that ,, , , and , where , are found. A new inclusion theorem is proved. Also, some open problems and conjectures are posed.