2012 On a Third-Order System of Difference Equations with Variable Coefficients
Stevo Stević, Josef Diblík, Bratislav Iričanin, Zdeněk Šmarda
Abstr. Appl. Anal. 2012: 1-22 (2012). DOI: 10.1155/2012/508523

## Abstract

We show that the system of three difference equations ${x}_{n+1}={a}_{n}^{(1)}{x}_{n-2}/({b}_{n}^{(1)}{y}_{n}{z}_{n-1}{x}_{n-2}+{c}_{n}^{(1)})$, ${y}_{n+1}={a}_{n}^{(2)}{y}_{n-2}/({b}_{n}^{(2)}{z}_{n}{x}_{n-1}{y}_{n-2}+{c}_{n}^{(2)})$, and ${z}_{n+1}={a}_{n}^{(3)}{z}_{n-2}/({b}_{n}^{(3)}{x}_{n}{y}_{n-1}{z}_{n-2}+{c}_{n}^{(3)})$, $n\in {\mathbb{N}}_{0}$, where all elements of the sequences ${a}_{n}^{(i)}$, ${b}_{n}^{(i)}$, ${c}_{n}^{(i)}$, $n\in {\mathbb{N}}_{0}$, $i\in \{1,2,3\}$, and initial values ${x}_{-j}$, ${y}_{-j}$, ${z}_{-j}$, $j\in \{0,1,2\}$, are real numbers, can be solved. Explicit formulae for solutions of the system are derived, and some consequences on asymptotic behavior of solutions for the case when coefficients are periodic with period three are deduced.

## Citation

Stevo Stević. Josef Diblík. Bratislav Iričanin. Zdeněk Šmarda. "On a Third-Order System of Difference Equations with Variable Coefficients." Abstr. Appl. Anal. 2012 1 - 22, 2012. https://doi.org/10.1155/2012/508523

## Information

Published: 2012
First available in Project Euclid: 14 December 2012

zbMATH: 1242.39011
MathSciNet: MR2926886
Digital Object Identifier: 10.1155/2012/508523