The Form of the Solutions of Nonlinear Difference Equations Systems

Volume 9, Issue 5, pp 3179--3196 http://dx.doi.org/10.22436/jnsa.009.05.107

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Authors

E. M. Elsayed - Mathematics Department, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia. - Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt. A. Alghamdi - Mathematics Department, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia. - Mathematics Department, University College of Umluj, Tabuk University, P. O. Box 741, Umluj 71491, Saudi Arabia.

Abstract

In this paper, we deal with the form of the solutions of the following nonlinear difference equations systems \[x_{n+1} =\frac{x_{n-7}}{1 + x_{n-7}y_{n-3}} ; y_{n+1} =\frac{y_{n-7}}{\pm 1 \pm x_{n-3}y_{n-7}};\] where the initial conditions \(x_{-7}; x_{-6}; x_{-5}; x_{-4}; x_{-3}; x_{-2}; x_{-1}; x_0; y_{-7}; y_{-6}; y_{-5}; y_{-4}; y_{-3}; y_{-2}; y_{-1}; y_0\) are real numbers.

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Keywords

• Difference equations
• system of difference equations
• solution of difference equation.

MSC

•  39A10.

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