Solvability of a system of nonlinear difference equations of higher order

Abstract

In this paper, we show that the following higher-order system of nonlinear difference equations, $x_{n=}frac{x_{n-kYn-k-l}}{Yn-l(a_n+b_nx_n-kYn-k-l)}$, $Y_{n=}frac{Y_{n-kxn-k-l}}{xn-l(a_n+b_nY_n-kxn-k-l)}$, $nin{mathbb{N}}_0$where k; l 2 N, (an)n2N0; (bn)n2N0; (n)n2N0; (n)n2N0and the initial values x􀀀i; y􀀀i , i = 1; k + l , are real numbers,can be solved and some results in the literature can be extended further. Also, by using these obtained formulas,we investigate the asymptotic behavior of well-defined solutions of the above difference equations system for the casek = 2; l = k .