Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2009; 46(4): 691-700

Printed July 1, 2009

https://doi.org/10.4134/BKMS.2009.46.4.691

Copyright © The Korean Mathematical Society.

Existence of solutions of quasilinear integrodifferential evolution equations in Banach spaces

Krishnan Balachandran and Dong Gun Park

Bharathiar University and Dong-A University

Abstract

We prove the local existence of classical solutions of quasilinear integrodifferential equations in Banach spaces. The results are obtained by using fractional powers of operators and the Schauder fixed-point theorem. An example is provided to illustrate the theory.

Keywords: existence of solution, quasilinear integrodifferential equation, analytic semigroup, fixed point theorem

MSC numbers: 34G20, 47H20