On some classes of linear difference equations with convergent solutions

Abstract

We present some classes of homogeneous linear difference equations with constant coefficients such that their associated characteristic polynomials have multiple zeros, and all solutions to the equations are convergent. The cases of the equations of third and fourth order are considered in detail, whereas in the case of equations of arbitrary order bigger than four, we present a subclass of such equations. We also show that the problem of calculating limits of solutions to the equations, when all the zeros of the characteristic polynomials are simple, is essentially folklore.