Solutions non oscillantes d’une équation différentielle et corps de Hardy  [ Non-oscillating solutions of a differential equation and Hardy fields ]
Annales de l'Institut Fourier, Volume 57 (2007) no. 6, p. 1825-1838

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.

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.

DOI : https://doi.org/10.5802/aif.2314
Classification:  34A26,  34C10,  34C08,  37C10
Keywords: oscillation, Hardy field, semi-algebraic, pfaffian 
@article{AIF_2007__57_6_1825_0,
     author = {Blais, Fran\c cois and Moussu, Robert and Sanz, Fernando},
     title = {Solutions non oscillantes d'une \'equation diff\'erentielle et corps de Hardy},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {57},
     number = {6},
     year = {2007},
     pages = {1825-1838},
     doi = {10.5802/aif.2314},
     mrnumber = {2377887},
     zbl = {1133.34007},
     language = {fr},
     url = {http://www.numdam.org/item/AIF_2007__57_6_1825_0}
}

Blais, François; Moussu, Robert; Sanz, Fernando. Solutions non oscillantes d’une équation différentielle et corps de Hardy. Annales de l'Institut Fourier, Volume 57 (2007) no. 6, pp. 1825-1838. doi : 10.5802/aif.2314. http://www.numdam.org/item/AIF_2007__57_6_1825_0/

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