On monotone solutions of some classes of difference equations

Abstract

We describe a method for finding monotone solutions of someclasses of difference equations converging to the correspondingequilibria. The method enables us to confirm three conjecturesposed by the present author in a talk, which are extensions ofthree 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 appliedalso when the parameters are variable.