一类线性差分方程的最优Ulam常数

On the best Ulam constant for a class of linear difference equations

摘要:

在一类线性差分方程的特征方程有且只有一个根的条件下，本文利用常数变易法给出该差分方程的通解结构，进而一定条件下通过构造了该差分方程的一个特别有界近似解. 最后，本文给出该差分方程的最优Ulam常数.

Abstract:

Suppose that the characteristic equation of the linear difference equation has a unique solution. We in this paper obtain the general solutions of the equation by using the method of variation of parameters. Under some conditions on the characteristic root, we further get the best Ulam constant of the equation by constructing a specific bounded approximate solution of the equation.