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Journal of Applied Mathematics and Stochastic Analysis
Volume 11 (1998), Issue 4, Pages 507-517
http://dx.doi.org/10.1155/S1048953398000410

Semilinear integro-differential equations with compact semigroups

1Indian Institute of Technology, Department of Mathematics, Kanpur 208 016, India
2Lucknow University, Department of Mathematics, Lucknow 226 007, India

Received 1 July 1996; Revised 1 May 1997

Copyright © 1998 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In this paper we study the local and global existence of mild solutions to a class of integro-differential equations in an arbitrary Banach space associated with the operators generating compact semigroups on the Banach space.