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

Stevo Stević

 Mathematical Institute of the Serbian Academy of Science Knez Mihailova 35/I, Beograd 11000, Serbia
Received 17 December 2005; Accepted 27 February 2006

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.