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.
