On some rational difference equations. (English) Zbl 1224.39014

From the introduction: R. P. Agarwal and E. M. Elsayed [Adv. Stud. Contemp. Math., Kyungshang 17, No. 2, 181–201 (2008; Zbl 1169.39001)] studied solutions of some particular cases of the following classes of the difference equations \[ x_{n+1}=ax_{n}+\frac {bx_{n}x_{n-3}}{cx_{n-2}+dx_{n-3}}\;(a,b,c,d\neq 0) \text{ and } x_{n+1}=x_{n}+\frac {dx_{n-l}x_{n-k}}{b-cx_{n-s}}, \] where \(k,l,s, n\in \mathbb {N}_0\) and \(a,b,c,d>0\). Explicit solutions of some subclasses of these equations are given. Our aim is to give short proofs of the main results of the above authors as well as to extend some of them.


39A20 Multiplicative and other generalized difference equations
39A23 Periodic solutions of difference equations


Zbl 1169.39001