Open Access

Semigroup Approach to Semilinear Partial Functional Differential Equations with Infinite Delay

Journal of Inequalities and Applications20072007:049125

DOI: 10.1155/2007/49125

Received: 6 November 2006

Accepted: 19 January 2007

Published: 21 February 2007

Abstract

We describe a semigroup of abstract semilinear functional differential equations with infinite delay by the use of the Crandall Liggett theorem. We suppose that the linear part is not necessarily densely defined but satisfies the resolvent estimates of the Hille-Yosida theorem. We clarify the properties of the phase space ensuring equivalence between the equation under investigation and the nonlinear semigroup.

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Authors’ Affiliations

(1)
National Engineering School of Applied Sciences (ENSA), University Ibn Zohr

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Copyright

© Hassane Bouzahir. 2007

This article is published under license to BioMed Central Ltd. 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.