Journal of Applied Mathematics and Stochastic Analysis 
Volume 2004 (2004), Issue 1, Pages 9-18
doi:10.1155/S1048953304212011

Periodic solutions for some partial functional differential equations

Rachid Benkhalti1 and Khalil Ezzinbi2

 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

Abstract

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.