Regularity of solutions of Sobolev type semilinear integrodifferential equations in Banach spaces

Abstract

In this article, we prove the existence of mild and classical solutions of Sobolev type semilinear integrodifferential equations of the form d /dt [Ex(t) = A[x(t) + ∫t 0 F(t - s) x (s)ds] + f(t, x(t)) in Banach spaces. The results are obtained by using the Banach contraction mapping principle and resolvent operator. An application is provided to illustrate the theory.