Journal of Inequalities and Applications
Volume 2007 (2007), Article ID 49125, 13 pages
Research Article

Semigroup Approach to Semilinear Partial Functional Differential Equations with Infinite Delay

Hassane Bouzahir

National Engineering School of Applied Sciences (ENSA), University Ibn Zohr, P.O. Box 1136, Agadir 80000, Morocco

Received 6 November 2006; Revised 16 January 2007; Accepted 19 January 2007

Academic Editor: Simeon Reich

Copyright © 2007 Hassane Bouzahir. 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.


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.