一次时滞微分方程零解的全局吸引性

The global attractivity of zero solutions for a class of functional differential equations

讨论了含有一个滞量的线性、非线性泛函微分方程零解的全局吸引性,对于线性泛函微分方程,x·(t)=-a(t)x(t)-b(t)x(t-τ),构造了Liapunov泛函,利用Liapunov稳定性定理,得到了线性泛函微分方程零解全局吸引的一个充分条件,同时将这一结论应用于非线性方程x·(t)=F(t,x(t),x(t-τ))和x·(t)=f(x(t-τ)),证明了在一定条件下它的零解是全局吸引的。

The global attractivity of zero solutions for linear and nonlinear functional differential equations of a delay is disscussed. For linear functional differential equation: x·(t)=-a(t)x(t)-b(t)x(t-τ), a Liapunov functional is constructed. By the theorem of Liapunov stability,a sufficient condition of the global attractivity of zero solutions for linear functional differential equations is obtained,and which is applied to the nonlinear functional differential equations: x·(t)=F((t,x(t),x(t-τ)) and x(-*2·(t)=F(x(t-τ)). That zero solution is global attractivity is proved under some conditions.