Existence of analytic solutions to analytic nonlinear q-difference equations ✩

– For linear q-difference equations ( |q| 6= 1), taking account of preceding results due to Birkhoff [4], the second author [37] and van der Put-Reversat [23] in the

SIBUYA, Multisummability of formal power series solutions of linear ordinary differential equations, Asymptotic Analysis, 5 (1991), 27-45..

Polynomials of one variable with their zeros as parameters We shall first study properties of fundamental solutions of ordinary dif- ferential operators whose corresponding

In particular we present an asymptotic functional equa- tion for potential asymptotic behaviour, and a theorem stating sufficient conditions for the existence of an actual solution

In fact, we prove in the next section that U is analytic, using a different expansion obtained by arborification, and that appears to be normally convergent.... Analytic part

Formal solutions of the heat equation, and their association to solutions obtained by inverse Laplace transform are studied in §3.. It is shown that power series are

We study the global Cauchy problem for nonlinear Schrödinger equations with cubic interactions of derivative type in space dimension n 3.. The global existence of small

in time if the initial function cp is analytic and sufficiently small. The purpose of this paper is twofold. 2) have a smoothing property if(p satisfies