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Soit φ: x → φ(x),x >> 0 une solution a l'infini d'une equation differentielle algebrique d'ordre n, P(x,y.y'....;y (n) ) = 0. Nous donnons un critere geometrique pour que les germes a l'infini de φ et de!a fonction identite sur R appartiennent a un meme corps de Hardy. Ce critere repose sur le concept de non oscillation.

Solutions non oscillantes d’une équation différentielle et corps de Hardy