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