Authors: Stević, Stevo 
Diblík, Josef
Iričanin, Bratislav
Šmarda, Zdenk
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: On a third-order system of difference equations with variable coefficients
Journal: Abstract and Applied Analysis
Volume: 2012
Issue Date: 20-Jun-2012
Rank: M21a
ISSN: 1085-3375
DOI: 10.1155/2012/508523
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 N 0, where all elements of the sequences a n(i), b n(i), c n(i), n N 0, i { 1,2, 3 }, and initial values x -j, y -j, z -j, j { 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.
Publisher: Hindawi
Project: Development Programme of The Ministry of Education,Youth and Sports of Czech Republic no. 25/16—PoZaP—Support for Foreign Teachers
Council of Czech Government, Grant MSM 00216 30519
Brno University of Technology, Grant FEKT-S-11-2-921
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