On a solvable p-dimensional system of nonlinear difference equations

Abstract

In this paper, we investigate the solutions of the following system of p−nonlinear difference equations

x⁽ⁱ⁾_n+1 = a⁽ⁱ⁾x^(i+1)mod(p)_n x^(i+1)mod(p)_n−2 / b⁽ⁱ⁾x⁽ⁱ⁾_n−1 +c⁽ⁱ⁾x^(i+1)mod(p)_n−2, n∈N₀, p∈N, i∈{1,..., p},

where N₀=N∪{0}, the sequences (a⁽ⁱ⁾), (b⁽ⁱ⁾), (c⁽ⁱ⁾), are non-zero real numbers and initial values x⁽ⁱ⁾_−j , j∈{0,1,2}, i∈{1,..., p}. Finally, we give some applications concerning aforementioned system of difference equations.