New solvable class of product-type systems of difference equations on the complex domain and a new method for proving the solvability

摘要

This paper continues the investigation of solvability of product-type systems of difference equations, by studying the following system with two variables: $$z_n=lpha z_{n-1}^aw_{n-2}^b,quad w_n=eta w_{n-3}^cz_{n-2}^d,quad ninmathbb{N}_0,$$ where $a,b,c,dinmathbb{Z}$, $lpha,etainmathbb{C}setminus{0}$, $w_{-3}, w_{-2}, w_{-1}, z_{-2}, z_{-1}inmathbb{C}setminus{0}$. It is shown that there are some important cases such that the system cannot be solved by using our previous methods. Hence, we also present a method different from the previous ones by which the solvability of the system is shown also in the cases.