一种变异的Lyapunov第二方法在脉冲微分方程中的应用

An Application of a Variation of the Lyapunov Second Method to Impulsive Differential Equations

研究脉冲微分方程 :x′=F(t,x) , t≠tk,△x(tk) =Ik(x(tk) ) ,x(t+ 0 ) =x0的零解 (其中 ,△x(tk) =x(t+ k) -x(tk) ,x(t+ k) =limt→t+kx(t) ) .对固定的脉冲点 ,扩展了比较性定理并运用到该方程 。

In this paper, the zero solution ofimpulsive differential systems x′=F(t,x),t≠t k, △x(t k)=I k(x(t k)), x(t + 0)=x 0 has been studied, where △x(t k)=x(t + k)-x(t k),x(t + k)= limt→t + kx(t). The comparison theorem is extended and applied withfixed moments of impulse, and the unstability theorem of the zero solution of perturbed impulsive differential equations is obtained.