Résumé
Using spectral theory we obtain sufficient conditions for the almost automorphy of bounded solutions to differential equations with piecewise constant argument of the form
x
′
(
t
)
=
A
(
t
)
x
(
[
t
]
)
+
f
(
t
)
,
t
∈
R
, where A(t) is an almost automorphy operator, f(t) is an
X
-valued almost automorphic function and
X
is a finite dimensional Banach space.