Carathéodory方程解的变差稳定性  

Variational Stability of the Solution to Carathéodory Equation

作　　者：李宝麟 王宁 Li Baolin;Wang Ning(College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,China)

机构地区：[1]西北师范大学数学与统计学院,甘肃兰州730070

出　　处：《甘肃科学学报》2020年第2期1-6,15,共7页Journal of Gansu Sciences

基　　金：国家自然科学基金项目(11061031)。

摘　　要：主要研究了Carathéodory方程的变差稳定性与渐近变差稳定性。在Carathéodory方程等价于广义常微分方程的基础上,借助广义常微分方程的稳定性理论,获得了Carathéodory方程解的变差稳定和渐近变差稳定的Lyapunov型定理。同时,将函数V满足的条件作适当修改,获得了Carathéodory方程的解关于部分变元的变差稳定和渐近变差稳定的Lyapunov型定理。This paper majorly studied the variational stability and asymptomatic variational stability of the Carathéodory equation.On the basis of the Carathéodory equation equivalent to the generalized normal differential equation,by virtue of the stability theory of the generalized ordinary differential equation,the Lyapunov-type theorem of the variational stability and asymptomatic variational stability of solution to Carathéodory equation was obtained.At the same time,the conditions met by function V were modified moderately to gain the Lyapunov-type theorem of the variational stability and asymptomatic variational stability of solution to Carathéodory equation in terms of part variables.

关 键 词：Carathéodory方程 变差稳定 渐近变差稳定 广义常微分方程 

分 类 号：O175.12[理学—数学]