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

Abstract:
In this article, we prove the existence and uniqueness of almost automorphic solutions to the non-autonomous evolution equation
$$ \frac{d}{dt}(u(t)-F_1(t,B_1u(t)))=A(t)(u(t)-F_1(t,Bu(t)))+F_2(t,u(t),B_2u(t)), \quad t\in \mathbb{R} $$
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.

Show me the PDF file (210 KB), TEX file, and other files for this article.

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

Return to the EJDE web page