On the perturbational global attractivity of nonautonomous delay differential equations (Q1292928)

The perturbed linear delay differential equation \[ x'(t)= -a(t)x(t-\tau)+ F(t,x_t) \] is considered. Different from most related work in the literature where \(a\) was regarded as a constant, the authors deal with the case, where \(a(t)\) is a continuous function. Several sufficient conditions are obtained for the zero solution to the equation to be globally attractive. These conditions extend and improve many known results for the constant coefficient case, and are ``sharp'' in some sense. It is pointed out that the method used can be applied to perturbed nonlinear equations of the form \[ x'(t)= G(t,x(t-\tau))+ F(t, x_t). \]