| 戴绍虞,潘一飞.一个向量形式的格朗沃尔(Gronwall)不等式*[J].数学年刊A辑,2023,44(3):303~314 |
| 一个向量形式的格朗沃尔(Gronwall)不等式* |
| A Vector Version of Gronwall’s Inequality |
| Received:August 29, 2021 Revised:March 25, 2023 |
| DOI：10.16205/j.cnki.cama.2023.0021 |
| 中文关键词: 格朗沃尔不等式, 微分方程, 稳定性, 唯一性 |
| 英文关键词:Gronwall’s inequality, Differential equations, Stability, Uniqueness |
| 基金项目:国家自然科学基金 (No.11671361) |
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| 中文摘要: |
| 本文证明了高阶微分算子的一个向量形式的格朗沃尔不等式.作为它的一个应用, 作者得到了具有奇异系数的$n$阶线性常微分方程系统在初始条件下解的稳定性和唯一性定理.作为它的另一个应用, 作者得到了n阶非线性常微分方程系统在初始条件下解的稳定性和唯一性定理. |
| 英文摘要: |
| In this note, the authors prove a vector version of Gronwall’s inequality for high order differential operators. As an application, the authors obtain the stability theorem and the uniqueness theorem of solutions of nth-order general linear systems of ordinary differential equations with singular coefficients in terms of initial values. As another application, the authors obtain the stability theorem and the uniqueness of solutions of n th-order nonlinear systems of ordinary differential equations in terms of initial values. |
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