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Solvability of a nonlinear three-dimensional system of difference equations with constant coefficients

  • Merve Kara EMAIL logo and Yasin Yazlik
Published/Copyright: October 4, 2021
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Abstract

In this paper, we show that the following three-dimensional system of difference equations

x n + 1 = y n x n 2 a x n 2 + b z n 1 , y n + 1 = z n y n 2 c y n 2 + d x n 1 , z n + 1 = x n z n 2 e z n 2 + f y n 1 , n N 0 ,

where the parameters a, b, c, d, e, f and the initial values xi, yi, zi, i ∈ {0, 1, 2}, are complex numbers, can be solved, extending further some results in the literature. Also, we determine the forbidden set of the initial values by using the obtained formulas. Finally, an application concerning a three-dimensional system of difference equations are given.

MSC 2010: 39A10; 39A20; 39A23
  1. (Communicated by Michal Fečkan)

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Received: 2020-03-31
Accepted: 2020-11-25
Published Online: 2021-10-04
Published in Print: 2021-10-26

© 2021 Mathematical Institute Slovak Academy of Sciences

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