International Journal of Mathematics and Mathematical Sciences
Volume 26 (2001), Issue 8, Pages 497-511

The method of averaging and functional differential equations with delay

Mustapha Lakrib

Département d'Informatique, Faculté des Sciences de l'Ingénieur, Université Djillali Liabès, B.P. 89, Sidi Bel Abbès 22000, Algeria

Received 2 October 2000

Copyright © 2001 Mustapha Lakrib. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We present a natural extension of the method of averaging to fast oscillating functional differential equations with delay. Unlike the usual approach where the analysis is kept in an infinite-dimensional Banach space, our analysis is achieved in n. Our results are formulated in classical mathematics. They are proved within Internal Set Theory which is an axiomatic description of nonstandard analysis.