Hukuhara domains and fundamental existence and uniqueness theorems for asymptotic solutions of Gevrey type. (English) Zbl 0699.34058

Ramis, Jean-Pierre; Sibuya, Yasutaka

Asymptotic Anal. 2, No. 1, 39-94 (1989).

The paper is based on the idea that for analytic differential equations in the complex domain the most suitable theory of asymptotics is the Gevrey theory consisting of Gevrey formal power series and Gevrey asymptotic expansions. After an Introduction dealing with some less general but useful “existence theorems” in the Gevrey theory, an extended presentation of Hukuhara domains is given. The exposition continues with fundamental theorems in classical cases ending with asymptotic solutions of Gevrey type.

Reviewer: W.Răsvan

MSC:

34E05	Asymptotic expansions of solutions to ordinary differential equations
34A25	Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc.
30E15	Asymptotic representations in the complex plane
34M99	Ordinary differential equations in the complex domain

Keywords:

analytic differential equations in the complex domain; Gevrey theory; Gevrey formal power series; Gevrey asymptotic expansions; Hukuhara domains