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.

中文翻译：

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关于某些类具有收敛解的线性差分方程

我们提出了一些具有恒定系数的齐次线性差分方程组，以使它们的相关特征多项式具有多个零，并且方程组的所有解都是收敛的。详细考虑了三阶和四阶方程的情况，而在任意阶的方程大于4的情况下，我们介绍了此类方程的子类。我们还表明，当特征多项式的所有零都简单时，计算方程解极限的问题本质上是民俗学。