Electronic Journal of Differential Equations,
Vol. 2006(2006), No. 56, pp. 1-14.
Title: Periodic solutions for some partial neutral functional
differential equations
Authors: Rachid Benkhalti (Pacific Lutheran Univ., Tacoma, WA, USA)
Abdelhai Elazzouzi (Univ. Cadi Ayyad, Marrakesh, Morocco)
Khalil Ezzinbi (Univ. Cadi Ayyad, Marrakesh, Morocco)
Abstract:
In this work, we study the existence of periodic solutions for
partial neutral functional differential equation.
We assume that the linear part is not necessarily densely defined
and satisfies the Hille-Yosida condition. In the nonhomogeneous
linear case, we prove that the existence of a bounded solution on
$\mathbb{R}^+$ implies the existence of a periodic solution.
In nonlinear case, we use the concept of boundedness and ultimate
boundedness to prove the existence of periodic solutions.
Submitted November 14, 2005. Published April 28, 2006.
Math Subject Classifications: 34C25, 34D40, 34K40, 34K60.
Key Words: Integral solutions; Hille-Yosida condition; boundedness;
ultimate boundedness; condensing map; Hale and Lunel's
fixed point theorem.