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THE NON-LOCAL CAUCHY PROBLEM FOR SEMILINEAR INTEGRODIFFERENTIAL EQUATIONS WITH DEVIATING ARGUMENT

Published online by Cambridge University Press:  20 January 2009

K. Balachandran  and
M. Chandrasekaran
K. Balachandran
Affiliation:
Department of Mathematics, Bharathiar University, Coimbatore-641 046, Tamil Nadu, IN
M. Chandrasekaran
Affiliation:
Department of Mathematics, Bharathiar University, Coimbatore-641 046, Tamil Nadu, IN
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Abstract

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The aim of this paper is to prove the existence and uniqueness of mild and classical solutions of the non-local Cauchy problem for a semilinear integrodifferential equation with deviating argument. The results are established by using the method of semigroups and the contraction mapping principle. The paper generalizes certain results of Lin and Liu.

AMS 2000 Mathematics subject classification: Primary 34K05; 34K30

Keywords

existence of solutionsresolvent operatorintegrodifferential equationdeviating argument
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 44 , Issue 1 , February 2001 , pp. 63 - 70
Copyright
Copyright © Edinburgh Mathematical Society 2001