On a solvable system of rational difference equations

Abstract

We show that the following system of difference equations

where , , , and sequences , , and are real, can be solved in closed form. For the case when the sequences , , and are constant and , we apply obtained formulas in the investigation of the asymptotic behaviour of well-defined solutions of the system. We also find domain of undefinable solutions of the system. Our results considerably extend and improve some recent results in the literature.

Keywords::

• system of difference equations
• solution in closed form
• asymptotic behaviour
• domain of undefinable solutions

2000 Mathematics Subject Classification::

• 2000 Primary 39A10
• 39A20

Acknowledgements

The second author was supported by the Grant P201/10/1032 of the Czech Grant Agency (Prague). The fourth author was supported by the grant FEKT-S-11-2-921 of Faculty of Electrical Engineering. This paper was also supported by the Serbian Ministry of Science projects III 41025, III 44006 and OI 171007.