**Complete guiding sets for a class of almost-periodic differential
equations**

with Ana I. Alonso and Rafael Obaya,

J. Differential Equations **208 **(**1**)
(2005), 124-146.

A functional differential equation admitting a complete guiding set
always has an

a priori bounded solution. The introduction of this concept and the idea of
reducibility

make it possible to apply a well known method for the autonomous case to a

non-autonomous problem. A previous result of Ortega and Tineo is extended to a

non-hyperbolic semilinear functional

coefficients in its lineal part. The non-hyperbolicity condition is established
in terms of

the Sacker-Sell spectrum of the associated linear system.