## Abstract and Applied Analysis

### On a Third-Order System of Difference Equations with Variable Coefficients

#### 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.

#### Article information

Source
Abstr. Appl. Anal., Volume 2012 (2012), Article ID 508523, 22 pages.

Dates
First available in Project Euclid: 14 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1355495726

Digital Object Identifier
doi:10.1155/2012/508523

Mathematical Reviews number (MathSciNet)
MR2926886

Zentralblatt MATH identifier
1242.39011

#### Citation

Stević, Stevo; Diblík, Josef; Iričanin, Bratislav; Šmarda, Zdeněk. On a Third-Order System of Difference Equations with Variable Coefficients. Abstr. Appl. Anal. 2012 (2012), Article ID 508523, 22 pages. doi:10.1155/2012/508523. https://projecteuclid.org/euclid.aaa/1355495726