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

Abstract

<p>In this article, we prove the existence of mild and classical solutions of Sobolev type semilinear integrodifferential equations of the form</p> <pre>d/dt [Ex(t) = A[x(t) + ∫^t₀ F(t - s)x(s)ds] + ƒ(t, x(t))</pre> <p>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.</p>