Discrete Dynamics in Nature and Society
Volume 2006 (2006), Article ID 53890, 9 pages
doi:10.1155/DDNS/2006/53890
On monotone solutions of some classes of difference equations
Mathematical Institute of the Serbian Academy of Science Knez Mihailova 35/I, Beograd 11000, Serbia
Received 17 December 2005; Accepted 27 February 2006
Copyright © 2006 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.
Abstract
We describe a method for finding monotone solutions of some
classes of difference equations converging to the corresponding
equilibria. The method enables us to confirm three conjectures
posed by the present author in a talk, which are extensions of
three conjectures by M. R. S. Kulenović and G. Ladas,
Dynamics of Second Order Rational Difference Equations.
With Open Problems and Conjectures. Chapman and Hall/CRC, 2002.
It is interesting that the method, in some cases, can be applied
also when the parameters are variable.