Instability of solution for the fourth order linear differential equation with varied coefficient

In this paper,we give some sufficient conditions of the instability for the fourth order linear differential equation with varied coefficient,at least one of the characteristic roots of which has positive real part,by means of Liapunov’s second method.     

具有周期系数的三阶线性微分方程解的稳定性

考虑三阶线性微分方程典十尸(才)典、口(,)李 *、才):二。dto dt‘dt(1)其中尸(t)、Q(t)、R(t)是t穴班主续周期函数,周期为。,且尸(t)还具有二阶连续导数. 通过变换、,户、J护Q口nj了‘、了,、。一牛{扮川‘:O=义e劲总可将方程(1)化为d3戈,,、口男—一十./生气不)—dt3 dt十B(t)%二O严1一3其中了主(矛)=口(t)一以尸(t) dt且刀(约、B汀)一也是才旧迩续周期函数,的稳定性,‘仑等价于方理组:。了二、_:、:、1〔12P(t).2。。,,、1。、。、力戈l少一It又子)一一一—十—了‘一气万)一—1一、不)以叮)‘ 3 dtzZ了3周期为。.因此下面我们只研…     

关于四阶变系数线性微分方程解的不稳定性

本文利用李雅普诺夫第二方法[1]给出了至少有一个特征根具有正实部的四阶变系数线性微分方程解的不稳定性的充分条件。     

关于三阶变系数线性微分方程解的不稳定性

文献[1]用李雅普诺夫第二方法证明了特征根均具有负实部的缓变系数动力系统的渐近稳定性.本文也用李雅普诺夫第二方法给出至少有一个特征根具有正实部的三阶变系数线性微分方程解的不稳定性的充分条件.     

INSTABILITY OF SOLUTION FOR THE THIRD ORDER LINEAR DIFFEBENTIAL EQUATION WITH VARIED COEFFICIENT

In reference [1] asymptotic stability of dynamic system with slowly changing coefficients for all characteristic roots which have negative real part has been proved by means of Liapunov's second method. In this paper, we give some sufficient conditions of the instability for the third order linear differential equation with varied coefficient, at least one of the characteristic roots of which has positive real part, by means of Liapunov's second method.