Solvability of a class of nonlinear system of difference equations with homogeneity

Abstract

We show that the following nonlinear system of difference equations of interest $x_n^{\left(l\right)}=\frac{a_l\prod _{j=1,j\ne l}^k{x}_{n-1}^{\left(j\right)}}{f(x_{n-1}^{\left(1\right)},\dots ,x_{n-1}^{\left(k\right)})},n\in N,l=\overline{1,k},$where $k\ge 2$, $a_j,x_0^{\left(j\right)}\in ℂ\setminus \left\{0\right\},$ $j=\overline{1,k},$ and the function $f:{ℂ}^k\to ℂ$ is homogeneous of degree $k-2$, is solvable in a closed form considerably extending some results in the literature.