Properties Of Solution Of Nonautonomous Linear Volterra Equations

Volterra integro-differential equations extensively appear in biology, physics, ecology, medicine and other research fields, which are playing a very important role in the natural sciences and various engineering modeling of the various issues, and have drawn the majority of scientific researcher to study.In this paper we mainly study the stability of nonautonomous linear Volterra integro-differential equation (:)First of all, we apply the resolvent operator R (t,α) of homogeneous Volterra integro-differential equation to derive the solution of nonhomogeneous Volterra integro-differential equation by the variation of parameters formula; Secondly, we characterize the total stability property of the zero solution of nonautonomous linear Volterra integro-differential equation in terms of the integrability of the resolvent operator; Finally, we establish that the equation (P,(?)) exist unique R-bounded solution.