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Journal of Applied Mathematics and Stochastic Analysis
Volume 4 (1991), Issue 2, Pages 117-128

An abstract inverse problem

Université de france-comté, Laboratory de Mathématiques, route de Gray, Besançon cédex 25030, France

Received 1 January 1990; Revised 1 October 1990

Copyright © 1991 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.


In this paper we consider an inverse problem that corresponds to an abstract integrodifferential equation. First, we prove a local existence and uniqueness theorem. We also show that every continuous solution can be locally extended in a unique way. Finally, we give sufficient conditions for the existence and a stability of the global solution.