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Turkish Journal of Mathematics

DOI

10.3906/mat-2001-40

Abstract

In this paper we solve the following system of difference equations \begin{equation*} x_{n+1}=\dfrac{z_{n-1}}{a+by_nz_{n-1}},\quad y_{n+1}=\dfrac{x_{n-1}}{a+bz_nx_{n-1}},\quad z_{n+1}=\dfrac{y_{n-1}}{a+bx_ny_{n-1}},\quad n\in \mathbb{N}_{0} \end{equation*} where parameters $a, b$ and initial values $x_{-1},x_{0},y_{-1},y_{0},z_{-1},z_{0}$ are nonzero real numbers, and give a representation of its general solution in terms of a specially chosen solutions to homogeneous linear difference equation with constant coefficients associated to the system.

Keywords

System of difference equations, general solution, representation of solutions

First Page

1263

Last Page

1288

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