On a Third‐Order System of Difference Equations with Variable Coefficients

Stevo Stević, Josef Diblík, Bratislav Iričanin and Zdeněk Šmarda

Abstract and Applied Analysis, 2012, vol. 2012, issue 1

Abstract: We show that the system of three difference equations xn+1=an(1)xn-2/(bn(1)ynzn-1xn-2+cn(1)), yn+1=an(2)yn-2/(bn(2)znxn-1yn-2+cn(2)), and zn+1=an(3)zn-2/(bn(3)xnyn-1zn-2+cn(3)), n ∈ ℕ0, where all elements of the sequences an(i), bn(i), cn(i), n ∈ ℕ0, 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.

Date: 2012
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https://doi.org/10.1155/2012/508523

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:508523

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