Electronic Journal of Differential Equations,
Vol. 2010(2010), No. 69, pp. 1-8.

Title: Almost automorphic solutions of neutral functional 
       differential equations
       
Authors: Gisele Massengo Mophou (Univ. des Antilles, Fouillole, Guadeloupe)
         Gaston M. N'Guerekata (Morgan State Univ., Baltimore MD, USA)

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.