Monomial summability and doubly singular differential equations

Mireille Canalis-Durand (1) , Jorge Mozo-Fernández , Reinhard Schäfke (2)

1 Université Paul Cézanne - Aix-Marseille 3
2 IRMA - Institut de Recherche Mathématique Avancée

In this work, we consider systems of differential equations that are doubly singular, i.e. that are both singularly perturbed and exhibit an irregular singular point. Under a condition that also guanrantees the existence of a unique formal solution, we show that this formal solution is monomially summable, i.e. summable with respect to the monomial in the independent variable and in the parameter in a (new) sense that will be defined. As a preparation, Poincaré asymptotics and Gevrey asymptotics in a monomial are studied.

Mots clés: ordinary differential equations; asymptotic expansions; summability; singular perturbation; irregular singular points

Domaines: Analyse classique [math.CA]; Variables complexes [math.CV]

Mireille Canalis-Durand, Jorge Mozo-Fernández, Reinhard Schäfke. Monomial summability and doubly singular differential equations. Journal of Differential Equations, 2007, 233, pp.485-511. ⟨10.1016/j.jde.2006.11.005⟩. ⟨hal-00124889⟩