no. 6
Solutions non oscillantes d’une équation différentielle et corps de Hardy
Blais, François1 ; Moussu, Robert1 ; Sanz, Fernando2
1 Université de Bourgogne IMB UFR Sciences et Tecniques 9 Avenue Alain Savary, BP47870 21004 Dijon cedex (France)
2 Universidad de Valladolid Depto. de Álgebra, Geometría y Topología Facultad de Ciencias E-47005 Valladolid (Spain)
Annales de l'Institut Fourier, Tome 57 (2007) no. 6, pp. 1825-1838.

Soit ϕ:x↦ϕ(x),x≫0 une solution à l’infini d’une équation différentielle algébrique d’ordre n, P(x,y,y ′ ,...,y (n) )=0. Nous donnons un critère géométrique pour que les germes à l’infini de ϕ et de la fonction identité sur ℝ appartiennent à un même corps de Hardy. Ce critère repose sur le concept de non oscillation.

Let ϕ:x↦ϕ(x),x≫0 be a solution of an algebraic differential equation of order n, P(x,y,y ′ ,...,y (n) )=0. We establish a geometric criterion so that the germs at infinity of ϕ and the identity function on ℝ belong to a common Hardy field. This criterion is based on the concept of non oscillation.

DOI : 10.5802/aif.2314
Classification : 34A26, 34C10, 34C08, 37C10
Mot clés : oscillation, corps de Hardy, semi-algébrique, pfaffien
Keywords: oscillation, Hardy field, semi-algebraic, pfaffian

Blais, François 1 ; Moussu, Robert 1 ; Sanz, Fernando 2

1 Université de Bourgogne IMB UFR Sciences et Tecniques 9 Avenue Alain Savary, BP47870 21004 Dijon cedex (France)
2 Universidad de Valladolid Depto. de Álgebra, Geometría y Topología Facultad de Ciencias E-47005 Valladolid (Spain) 
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Blais, François; Moussu, Robert; Sanz, Fernando. Solutions non oscillantes d’une équation différentielle et corps de Hardy. Annales de l'Institut Fourier, Tome 57 (2007) no. 6, pp. 1825-1838. doi : 10.5802/aif.2314. https://aif.centre-mersenne.org/articles/10.5802/aif.2314/

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