Multisummability of Formal Power Series Solutions of Nonlinear MeromorphicDifferential Equations

摘要

A full proof of a theorem that power series solutions of nonlinear meromorphicdifferential equations are multisummable, is given. A concise review of the definition of multisummability is included. A nonlinear ordinary differential equation is reduced to a normal formal from which the Newton polygon can be read off. Convolution equations which arise by application of some form of Borel transformation are derived. Lemmas are proved by means of the contraction principle, linearization of the convolution equations and a majorant equation. Multisum solutions are compared on different sides of singular directions in view of the Stokes phenomenon.