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 differential equation with almost-periodic
coefficients in its lineal part. The non-hyperbolicity condition is established in terms of
the Sacker-Sell spectrum of the associated linear system.