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An Analytic Proof of the Malgrange Theorem on the Convergence of Formal Solutions of an ODE

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Abstract

We propose an analytic proof of the Malgrange theorem concerning a sufficient condition of the convergence of a formal power series satisfying an ordinary differential equation. The proof is based on the majorant method and allows to estimate the radius of convergence of such a series.

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Acknowledgements

The work is supported by the Russian Foundation for Basic Research (grant no. 12-01-31421 mol_a) and the Russian Federation President program for the support of young scientists (grant no. MK-4594.2013.1).

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Authors and Affiliations

  1. Institute for Information Transmission Problems of the Russian Academy of Sciences, Bolshoy Karetny per. 19, Moscow, Russia

    Renat Gontsov

  2. Keldysh Institute of Applied Mathematics of the Russian Academy of Sciences, Miusskaya sq. 4, Moscow, Russia

    Irina Goryuchkina

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  1. Renat Gontsov
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  2. Irina Goryuchkina
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Correspondence to Irina Goryuchkina.

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Gontsov, R., Goryuchkina, I. An Analytic Proof of the Malgrange Theorem on the Convergence of Formal Solutions of an ODE. J Dyn Control Syst 22, 91–100 (2016). https://doi.org/10.1007/s10883-014-9254-3

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  • DOI: https://doi.org/10.1007/s10883-014-9254-3

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