On a solvable class of product-type systems of difference equations

Abstract

It is shown that the following class of systems of difference equations (Formula Presented) where a, b, c, d ∈ Z, α, β, z−2, z−1, z0, w0 ∈ C \ {0}, is solvable, continuing our investigation of classification of solvable product-type systems with two dependent variables. We present closed form formulas for solutions to the systems in all the cases. In the main case, when bd ≠ 0, a detailed investigation of the form of the solutions is presented in terms of the zeros of an associated polynomial whose coefficients depend on some of the parameters of the system.