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

Stevo Stević | Zendy; Josef Diblı́k | Zendy; Bratislav Iričanin | Zendy; Zdeněk Šmarda | Zendy

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

Author(s) -

Stevo Stević,

Josef Diblı́k,

Bratislav Iričanin,

Zdeněk Šmarda

Publication year - 2012

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2012/508523

Subject(s) - mathematics , third order , order (exchange) , mathematical analysis , variable (mathematics) , philosophy , theology , finance , economics

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

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