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Korean Mathematical Society BKMS

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Bull. Korean Math. Soc. 2002; 39(4): 561-569

Printed December 1, 2002

Copyright © The Korean Mathematical Society.

Nonlocal Cauchy problem for Sobolev type functional integrodifferential equation

K. Balachandran and Jong Yeoul Park

Bharathiar University, Pusan National University

Abstract

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In this paper we prove the existence and uniqueness of a mild solution of a functional differential equation of Sobolev type with nonlocal condition using the semigroup theory and the Banach fixed point principle.

Keywords: $C_0$ semigroup, Banach fixed point principle, functional integrodifferential equation, Sobolev type, nonlocal condition

MSC numbers: 34G20, 47H20

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