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Discrete Dynamics in Nature and Society
Volume 2006 (2006), Article ID 53890, 9 pages

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.


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.