[Simplification uniforme au voisinage d'un point tournant]
Nous donnons une version analytique d'un théorème formel dû à R.J. Hanson et D.L. Russell. Il s'agit d'un résultat de simplification uniforme au voisinage d'un point tournant pour des équations différentielles linéaires singulièrement perturbées du second ordre, qui généralise un théorème connu de Y. Sibuya.
We give an analytic version of a formal theorem due to R.J. Hanson and D.L. Russell. This version is a result of uniform simplification in a full neighborhood of a turning point for linear singularly perturbed differential equations of the second order, which generalizes a well-known theorem of Y. Sibuya.
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@article{CRMATH_2015__353_9_789_0,
author = {Hulek, Charlotte},
title = {Uniform simplification in a full neighborhood of a turning point},
journal = {Comptes Rendus. Math\'ematique},
pages = {789--793},
publisher = {Elsevier},
volume = {353},
number = {9},
year = {2015},
doi = {10.1016/j.crma.2015.06.011},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2015.06.011/}
}
TY - JOUR AU - Hulek, Charlotte TI - Uniform simplification in a full neighborhood of a turning point JO - Comptes Rendus. Mathématique PY - 2015 SP - 789 EP - 793 VL - 353 IS - 9 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2015.06.011/ DO - 10.1016/j.crma.2015.06.011 LA - en ID - CRMATH_2015__353_9_789_0 ER -
%0 Journal Article %A Hulek, Charlotte %T Uniform simplification in a full neighborhood of a turning point %J Comptes Rendus. Mathématique %D 2015 %P 789-793 %V 353 %N 9 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2015.06.011/ %R 10.1016/j.crma.2015.06.011 %G en %F CRMATH_2015__353_9_789_0
Hulek, Charlotte. Uniform simplification in a full neighborhood of a turning point. Comptes Rendus. Mathématique, Tome 353 (2015) no. 9, pp. 789-793. doi : 10.1016/j.crma.2015.06.011. http://www.numdam.org/articles/10.1016/j.crma.2015.06.011/
[1] Composite asymptotic expansions and turning points of singularly perturbed ordinary differential equations, C. R. Acad. Sci. Paris, Ser. I, Volume 348 (2010) no. 23–24, pp. 1273-1277
[2] Composite Asymptotic Expansions, Lecture Notes in Mathematics, vol. 2066, Springer, 2013
[3] Classification and reduction of second-order systems at a turning point, J. Math. Phys., Volume 46 (1967), pp. 74-92
[4] Classification and reduction of second-order systems at a turning point, Dyn. Syst. (2014) (Université de Strasbourg, France)
[5] Zur Parameterabhängigkeit bei Differentialgleichungen, J. Reine Angew. Math., Volume 361 (1985), pp. 1-10
[6] Uniform simplification in a full neighborhood of a transition point, Mem. Amer. Math. Soc., Volume 149 (1974)
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