The Existence And Uniqueness Of Solution Of Two Kinds Of Integro-differential Equations

Firstly, the paper is concerned with the existence and uniqueness of the solution of the following Volterra integro-differential equitions for Hille-Yosida operatorUsing the contraction mapping principle , the existence and uniqueness of strict solution of ( IDE ) are prooved.Secondly, the paper is concerned with the local existence and uniqueness of the solution of quasilinear integro-differential evolution equitions with finite delay in Banach space of the form where is the infinitesimal generator of an analytic semigroup in a Banach space uniformly bounded and continuous in all of its arguments and is continuous.Here of continuous functions from [ ?r, to endowded with the sup-norm.Using the parabolic evolution systems, fractional powers of operator and the Schauder fixed point theorem, the local existence and uniqueness of are given. (Q IDE)...