Electron. J. Diff. Equ., Vol. 2010(2010), No. 69, pp. 1-8.

Almost automorphic solutions of neutral functional differential equations

Gisele Massengo Mophou, Gaston M. N'Guerekata

In this article, we prove the existence and uniqueness of almost automorphic solutions to the non-autonomous evolution equation
 \quad t\in \mathbb{R}
where $A(t)$ generates a hyperbolic evolution family $U(t,s)$ (not necessarily periodic) in a Banach space, and $B_1,B_2$ are bounded linear operators. The results are obtained by means of fixed point methods.

Submitted May 25, 2009. Published May 17, 2010.
Math Subject Classifications: 34K05, 34A12, 34A40.
Key Words: Neutral differential equation; almost automorphic functions; almost periodic functions; exponentially stable semigroup; semigroup of linear operators.

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Gisèle M. Mophou
Département de Mathématiques et Informatique
Université des Antilles et de La Guyane, Campus Fouillole 97159 Pointe-à-Pitre Guadeloupe (FWI)
email: gmophou@univ-ag.fr
Gaston M. N'Guérékata
Department of Mathematics
Morgan State University
1700 E. Cold Spring Lane, Baltimore, MD 21251, USA
email: Gaston.N'Guerekata@morgan.edu, nguerekata@aol.com

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