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<inf>n</inf>^(l)=[Formula presented],n∈N,l=1,k¯,where k≥2, a<inf>j</inf>,x<inf>0</inf>^(j)∈ℂ∖{0}, j=1,k¯, and the function f:ℂ^k→ℂ is homogeneous of degree k−2, is solvable in a closed form considerably extending some results in the literature.