Electronic Journal of Differential Equations,
Vol. 2003(2003), No. 114, pp. 1-8.

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

Authors: Krishnan Balachandran (Bharathiar Univ., India)
         Subbarayan Karunanithi (Kongunadu Arts and Science College, India)

Abstract: 
 In this article, we prove the existence of mild and classical
 solutions of Sobolev type semilinear integrodifferential equations
 of the form
 $$
 \frac{d}{dt}[Ex(t)] = A[x(t)+\int_0^tF(t-s)x(s)ds]+f(t,x(t))
 $$
 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.
   
Submitted July 17, 2003. Published November 20, 2003.
Math Subject Classifications: 34G20.
Key Words: Classical solution; semilinear integrodifferential equation;
           resolvent operator;  fixed point theorem.