| 一类线性差分方程的最优Ulam常数 |
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| 引用本文： | 侯牧林,徐冰. 一类线性差分方程的最优Ulam常数[J]. 四川大学学报(自然科学版), 2022, 59(3): 031002-20 |
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| 作者姓名： | 侯牧林 徐冰 |
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| 作者单位： | 四川大学数学学院,四川大学数学学院 |
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| 基金项目： | 国家自然科学基金（11771307） |
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| 摘 要： | 在线性差分方程xn+p=a1xn+p-1+…+apxn的特征方程有且只有一个根r的条件下，本文利用常数变易法给出了该差分方程的通解结构，进而在|r|>1的条件下构造了该差分方程的一个特别有界近似解.最后，本文给出了该差分方程的最优Ulam常数.
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| 关 键 词： | 通解 Hyers-Ulam稳定性 最优Ulam常数 |
| 收稿时间： | 2021-11-03 |
| 修稿时间： | 2021-12-14 |
On the best Ulam constant for a class of linear difference equations |
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| HOU Mu-Lin and XU Bing. On the best Ulam constant for a class of linear difference equations[J]. Journal of Sichuan University (Natural Science Edition), 2022, 59(3): 031002-20 |
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| Authors: | HOU Mu-Lin and XU Bing |
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| Affiliation: | School of Mathematics Sichuan University,School of Mathematics, Sichuan University |
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| 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. |
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