On monotone solutions of some classes of difference equations

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. Kulenovic 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.