[Une Note sur les équations fonctionnelles scalaires non-autonomes à petit retard]
Dans cette Note on montre que les ensembles minimaux pour les semiflots engendrés par les solutions des équations fonctionnelles non-autonomes à petit retard sont des extensions presque automorphes de la base. Ce résultat n'est plus vrai pour un retard arbitraire. C'est la condition sur le retard qui garantit l'existence de solutions dites solutions spéciales. Ces solutions-ci nous permettent de considérer notre problème au moyen d'un autre plus facile relatif aux équations différentielles ordinaires.
We prove that the minimal sets in the skew-product semiflows generated from a non-autonomous scalar functional differential equation with a small delay are all almost automorphic extensions of the base. This result is not true for arbitrary delay equations. The point is that, for a small delay, so-called special solutions exist and permit us to tackle the problem by means of some related scalar ODE's for which the study is much simpler.
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@article{CRMATH_2005__340_2_155_0,
author = {Alonso, Ana I. and Obaya, Rafael and Sanz, Ana M.},
title = {A {Note} on non-autonomous scalar functional differential equations with small delay},
journal = {Comptes Rendus. Math\'ematique},
pages = {155--160},
publisher = {Elsevier},
volume = {340},
number = {2},
year = {2005},
doi = {10.1016/j.crma.2004.11.027},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2004.11.027/}
}
TY - JOUR AU - Alonso, Ana I. AU - Obaya, Rafael AU - Sanz, Ana M. TI - A Note on non-autonomous scalar functional differential equations with small delay JO - Comptes Rendus. Mathématique PY - 2005 SP - 155 EP - 160 VL - 340 IS - 2 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2004.11.027/ DO - 10.1016/j.crma.2004.11.027 LA - en ID - CRMATH_2005__340_2_155_0 ER -
%0 Journal Article %A Alonso, Ana I. %A Obaya, Rafael %A Sanz, Ana M. %T A Note on non-autonomous scalar functional differential equations with small delay %J Comptes Rendus. Mathématique %D 2005 %P 155-160 %V 340 %N 2 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2004.11.027/ %R 10.1016/j.crma.2004.11.027 %G en %F CRMATH_2005__340_2_155_0
Alonso, Ana I.; Obaya, Rafael; Sanz, Ana M. A Note on non-autonomous scalar functional differential equations with small delay. Comptes Rendus. Mathématique, Tome 340 (2005) no. 2, pp. 155-160. doi : 10.1016/j.crma.2004.11.027. http://www.numdam.org/articles/10.1016/j.crma.2004.11.027/
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