初始时刻不同的非线性微分系统的严格稳定性  

Strict Stability of a Nonlinear Differential System with Different Initial Times

作　　者：郭淑利[1] 杨金根[1] 

机构地区：[1]信阳师范学院数学与信息科学学院,河南信阳464000

出　　处：《河南大学学报（自然科学版）》2016年第6期750-756,共7页Journal of Henan University:Natural Science

基　　金：国家自然科学基金资助项目(11271314);河南省自然科学基金资助项目(142300410440)

摘　　要：运用微分不等式技巧分析初始时刻不同的非线性微分方程(组)的严格稳定性和严格实用稳定性.把初始时刻不同的非线性微分系统实用稳定性的有关概念推广至初始时刻不同的非线性微分系统的严格实用稳定性,利用两个类Lyapunov函数得到了初始时刻不同的非线性微分系统严格实用稳定性的充分条件,最后给出了比较定理,它在证明初始时刻不同的非线性微分方程(组)的各种实用稳定性时是非常方便实用的.This paper investigated strict stability and strictly practical stability of a nonlinear differential system with different initial times by using differential inequality techniques. Some concepts of practical stability of the solutions to the nonlinear differential equation（s） with different initial times were developed to strictly practical stability, and several sufficient conditions were given for strictly practical stability by employing two Lyapunov like functions. In the end, a comparison theorem was presented which was useful in proving a variety of practical stability of solutions to nonlinear differential equation（s） with different initial times.

关 键 词：初始时刻 非线性微分系统 严格稳定性 严格实用稳定性 

分 类 号：O175.12[理学—数学]