Product-type system of difference equations with a complex structure of solutions

Abstract

The solvability of the following system of difference equations (Formula presented.) where a, b, c, d∈ Z, α, β, w− 2, w− 1, w0, z− 2, z− 1, z0∈ C∖ {0} , is studied in detail by using several methods. The system has the most complex structure of solutions of all the related systems studied so far, and some of the forms of solutions appear for the first time.