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.