Electron. J. Diff. Equ., Vol. 2010(2010), No. 128, pp. 1-14.

Weighted pseudo-almost periodic solutions for some neutral partial functional differential equations

Khalil Ezzinbi, Samir Fatajou, Gaston M. N'Guerekata

Abstract:
In this work, we give sufficient conditions for the existence and uniqueness of a weighted pseudo-almost periodic solutions for some neutral partial functional differential equations. Our working tools are based on the variation of constant formula and the spectral decomposition of the phase space. To illustrate our main result, we propose to study the existence and uniqueness of a weighted pseudo-almost periodic solution for some neutral model arising in physical systems.

Submitted May 1, 2010. Published September 8, 2010.
Math Subject Classifications: 34G20, 43A60.
Key Words: Neutral partial functional differential equation; spectral decomposition; weighted pseudo-almost periodic solution; exponential dichotomy.

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Khalil Ezzinbi
Université Cadi Ayyad, Faculté des Sciences Semlalia
Département de Mathématiques, B.P. 2390, Marrakech, Morocco
email: ezzinbi@ucam.ac.ma
Samir Fatajou
Université Cadi Ayyad, Faculté des Sciences Semlalia
Département de Mathématiques, B.P. 2390, Marrakech, Morocco
email: s.fatajou@ucam.ac.ma
Gaston M. N'Guérekata
Department of Mathematics, Morgan State University
1700 East Cold Spring Lane, Baltimore, MD 21251, USA
email: Gaston.N'Guerekata@morgan.edu, nguerekata@aol.com

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