Solving a class of nonautonomous difference equations by generalized invariants

Abstract

By using generalized invariants, we describe a method for solving a class of higher-order nonautonomous difference equations. Solvability of the equations of order two, three, and four are studied in detail. Our results explain and extend some problems in the literature. As far as we know, the case when the order is four is considered for the first time in this paper. For the equations of second order, we also give an explanation how they can be obtained in a natural way.