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Article Dans Une Revue Journal of Dynamical and Control Systems Année : 2020

Gevrey Properties and Summability of Formal Power Series Solutions of Some Inhomogeneous Linear Cauchy-Goursat Problems

Résumé

In this article, we investigate the Gevrey and summability properties of the formal power series solutions of some inhomogeneous linear Cauchy-Goursat problems with analytic coefficients in a neighborhood of (0 , 0) ∈ ℂ2. In particular, we give necessary and sufficient conditions under which these solutions are convergent or are k-summable, for a convenient positive rational number k, in a given direction.
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Dates et versions

hal-03993065 , version 1 (27-03-2023)

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Pascal Remy. Gevrey Properties and Summability of Formal Power Series Solutions of Some Inhomogeneous Linear Cauchy-Goursat Problems. Journal of Dynamical and Control Systems, 2020, 26 (1), pp.69-108. ⟨10.1007/s10883-019-9428-0⟩. ⟨hal-03993065⟩

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