一个向量形式的格朗沃尔(Gronwall)不等式  

A Vector Version of Gronwall's Inequality

作　　者：戴绍虞[1] 潘一飞 DAI Shaoyu;PAN Yifei(Department of Mathematics,Jinling Institute of Technology,Nanjing 211169,China;Department of Mathematical Sciences,Purdue University Fort Wayne,Fort Wayne 46805-1499,USA)

机构地区：[1]金陵科技学院数学系,南京211169 [2]普渡大学韦恩堡校区数学系,美国韦恩堡46805-1499

出　　处：《数学年刊（A辑）》2023年第3期303-314,共12页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.11671361)的资助。

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.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 diferential equations with singular coefficients in terms of initial values.As another application,the authors obtain the stability theorem and the uniqueness of solutions of nth-order nonlinear systems of ordinary differential equations in terms of initial values.

关 键 词：格朗沃尔不等式 微分方程 稳定性 唯一性 

分 类 号：O175[理学—数学]