Solution formelle Gevrey d'une équation singulièrement perturbée : le cas multidimensionel

Gevrey solutions of singularly perturbed differential equations, an extension to the non-autonomous case

“…to be invertible on D r2 (θ 0 ). In this case, the function k is uniquely determined by equation (6). In addition, a holomorphic solution y is given by…”

“…The modified Nagumo norm (see [15,22]), was first used in the context of singularly perturbed equations by R. Schäfke in [19] and by Canalis-Durand in [5,7,6].…”

“…Let us pose g = P 1 (f ), a = P 2 (f ). As in the equation (6), we have that for all j = 0, ..., m − 1,…”

Multisummability of Formal Solutions of Singular Perturbation Problems

“…More recently, one has begun to investigate Gevrey properties of # x x; or discuss its (multi)summability. Of the recent articles containing results in this direction, we mention Wallet [12,13], Canalis-Durand [4], Beno# ı ıt et al [3], Sibuya [11], and Canalis-Durand et al [5].…”

Asymptotic analysis of the peeling-off point of a French duck

“…Eckhaus was apparently the first to attempt to analyze a duck trajectory in the traditional setting of hard analysis. More recent work on problems in this general area appear in [4], [8], and [15]. Much of the work is based on nonstandard analysis, but tha,t in [15] uses a classical approach due to Pontryagin.…”