关于一类变系数线性微分方程组零解渐近稳定性的一个判别法则

来源期刊：中南大学学报(自然科学版)1979年第3期

论文作者：芮嘉诰

文章页码：135 - 144

关键词：变系数线性微分方程； 零解渐近稳定性； 判别法则； 渐近稳定性定理； 充分条件； 中立型； 变系数线性系统； 微分差分方程； 直接利用； 缓变系数

摘    要：本文直接利用dV/dt<0的方法,推出一类变系数线性微分方程组零解为渐近稳定性的充分条件,这个条件推广了文[3]的结果,对于具有非缓变系数的线性系统,在定理的条件下也可适用。本文并利用文[3]的结论将上述结果推广到滞后型微分差分方程(中立型)中去,也得到了一个充分条件。

Abstract: It is said in this article that the expression dv/dt <0 is made use of tofind the condition sufficient to identify the asympototic stability of zero solution of a group of Linear Differential Equations with varying coefficients This condition has developed the results of reference[3]and in accordance with its principle it may be also applied to the linear systems with urgently varying coefficients.Based on the conclusion of reference [5],the results mentioned above are extended to the application of the retarted type of differential-difference equations (neutral type) and favourable conditions have, been found.