Uniform complete guiding sets for finite-delay differential equations

with Rafael Obaya,

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.