International Journal of Mathematics and Mathematical Sciences
Volume 26 (2001), Issue 8, Pages 497-511
doi:10.1155/S0161171201010407
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
Abstract
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 ℝn. Our results are formulated in classical mathematics. They are proved within Internal Set Theory which is an axiomatic description of nonstandard analysis.