Electron. J. Diff. Eqns., Vol. 2003(2003), No. 114, pp. 1-8.

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

Krishnan Balachandran & Subbarayan Karunanithi

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.

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Krishnan Balachandran
Department of Mathematics
Bharathiar University
Coimbatore-641 046, India
email: balachandran_k@lycos.com
Subbarayan Karunanithi
Department of Mathematics
Kongunadu Arts and Science College
Coimbatore-641029, India
email: sknithi1957@yahoo.co.in

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