Ordinary differential equations
Uniform simplification in a full neighborhood of a turning point
Comptes Rendus. Mathématique, Volume 353 (2015) no. 9, pp. 789-793.

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.

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.

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DOI: 10.1016/j.crma.2015.06.011
Hulek, Charlotte 1

1 IRMA, UMR 7501, 7, rue René-Descartes, 67084 Strasbourg cedex, France
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Hulek, Charlotte. Uniform simplification in a full neighborhood of a turning point. Comptes Rendus. Mathématique, Volume 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/

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[2] Fruchard, A.; Schäfke, R. Composite Asymptotic Expansions, Lecture Notes in Mathematics, vol. 2066, Springer, 2013

[3] Hanson, R.J.; Russell, D.L. Classification and reduction of second-order systems at a turning point, J. Math. Phys., Volume 46 (1967), pp. 74-92

[4] Hulek, C. Classification and reduction of second-order systems at a turning point, Dyn. Syst. (2014) (Université de Strasbourg, France)

[5] Schäfke, F.W.; Schäfke, R. Zur Parameterabhängigkeit bei Differentialgleichungen, J. Reine Angew. Math., Volume 361 (1985), pp. 1-10

[6] Sibuya, Y. Uniform simplification in a full neighborhood of a transition point, Mem. Amer. Math. Soc., Volume 149 (1974)

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