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 Differential 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.