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

Abstract

Let \phi: x -> \phi (x), x > 0 be a solution of an algebraic differential equation of order n, P(x, y, y0, . . . , y(n)) = 0. We establish a geometric criterion so that the germs at infinity of \phi and the identity function on R belong to a common Hardy field. This criterion is based on the concept of non oscillation.