关于三阶变系数线性微分方程解的不稳定性

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Instability of Solution for the Third Order Linear Differential Equation with Varied Coefficient

摘要: 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.

Abstract: 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.

[1]	秦元勋、王联、王慕秋,缓变系数动力系统的译动稳定性,中国科学,专辑(I)(1979),242-253
[2]	秦元勋、王慕秋、王联,《运动稳定性理论与应用》,科学出版社(1981),
[3]	Курощ А.Г,《高等代数教程》,商务印书馆(1953).