%0 Journal Article
%T Almost automorphic solutions of neutral functional differential equations
%A Gisele M. Mophou
%A Gaston M. N'Guerekata
%J Electronic Journal of Differential Equations
%D 2010
%I Texas State University
%X In this article, we prove the existence and uniqueness of almost automorphic solutions to the non-autonomous evolution equation $$ frac{d}{dt}(u(t)-F_1(t,B_1u(t)))=A(t)(u(t)-F_1(t,Bu(t)))+F_2(t,u(t),B_2u(t)), quad tin mathbb{R} $$ 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.
%K Neutral differential equation
%K almost automorphic functions
%K almost periodic functions
%K exponentially stable semigroup
%K semigroup of linear operators
%U http://ejde.math.txstate.edu/Volumes/2010/69/abstr.html