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.