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