Journal of Applied Mathematics and Stochastic Analysis
Volume 2004 (2004), Issue 1, Pages 9-18
Periodic solutions for some partial functional differential
1Department of Mathematics, Pacific Lutheran University, Tacoma 98447, WA, USA
2Département de Mathématiques, Faculté des Sciences Semlalia, Université Cadi Ayyad, B.P. 2390, Marrakech 40000, Morocco
Received 11 December 2002; Revised 25 August 2003
Copyright © 2004 Rachid Benkhalti 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.
We study the existence of a periodic solution for some partial
functional differential equations. We assume
that the linear part is nondensely defined and satisfies the
Hille-Yosida condition. In the nonhomogeneous linear case, we
prove the existence of a periodic solution under the existence of
a bounded solution. In the nonlinear case, using a fixed-point
theorem concerning set-valued maps, we establish the existence of
a periodic solution.