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

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.