Journal of Applied Mathematics and Stochastic Analysis
Volume 2005 (2005), Issue 3, Pages 259-274

𝒞-total stability and almost periodicity for some partial functional differential equations with infinite delay

Abdelhai Elazzouzi and Khalil Ezzinbi

Département de Mathématiques, Faculté des Sciences Semlalia, Université Cadi Ayyad, B.P. 2390, Marrakech 4000, Morocco

Received 13 May 2004; Revised 2 September 2004

Copyright © 2005 Abdelhai Elazzouzi and Khalil Ezzinbi. 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 study the existence of an almost periodic solution for some partial functional differential equation with infinite delay. We assume that the linear part is nondensely defined and satisfies the known Hille-Yosida condition. We prove if the null solution of the homogeneous equation is 𝒞-total stable, then the nonhomogeneous equation has an almost periodic solution.