Uniform complete guiding sets for finite-delay differential equations

with Rafael Obaya,
in: Equadiff 2003: International Conference on Difference Equations, 848-855,

eds: F. Dumortier, H. W. Broer, J. Mawhin, A. Vanderbauwhede, S. Verduyn Lunel,
World Scientific Publishing, Singapore, 2005.

A technical property based on comparison with ODEs is added to the definition of
uniform complete guiding set in order to assure the existence of an a priori bounded
solution for a class of finite-delay equations. Some examples constitute a sample of
the applicability of this result. In particular, Landesman-Lazer type conditions
guaranteing a bounded solution for an n-order escalar equation are refined.