一类非驻定系统零解的稳定性

STABILITY FOR THE ZERO SOLUTIONS OF A CLASS oF NONAUTONOMOUS SYSTEMS

本文研究了线性微分方程dx/dt=A(t)x及一般形式的非线性微分方程组dx/dt=A(t,x)x的零解在Lyapunov意义下的稳定性问题,并给出了零解稳定、渐近稳定和不稳定的判定准则.

In this paper we disuss the stability of the zero solutions of the lincar systemdx/dt = A(t)xsnd the general nonlinear systemdx/dt = A(t,x)xAnd we give the discriminating theorcm for the stability, asymptotic stability and unstability of the zero solutions.