Differential Puiseux theorem in generalized series fields of finite rank

Details Differential Puiseux theorem in generalized series fields of finite rank Differential Puiseux theorem in generalized series fields of finite rank

2009-02-10

arxiv.org/abs/0902.1758v2

Annales de la facult\'e des sciences de Toulouse S\'er. 6, 20 no. 2 (2011), p. 247-293

Mathematics

Classical Analysis and ODEs

37 pages

Scientific paper

We study differential equations $F(y,...,y^{(n)})=0$ where $F(Y_0,...,Y_n)$ is a formal series in $Y_0,...,Y_n$ with coefficients in some field of \emph{generalized power series} $\mathds{K}_r$ with finite rank $r\in\mathbb{N}^*$. Our purpose is to understand the connection between the set of exponents of the coefficients of the equation $\textrm{Supp} F$ and the set $\textrm{Supp} y_0$ of exponents of the elements $y_0\in\mathds{K}_r$ that are solutions.

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