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Mat. Sb., 2019, Volume 210, Number 9, Pages 3–18 (Mi msb9064)  

This article is cited in 1 scientific paper (total in 1 paper)

Convergence of formal Dulac series satisfying an algebraic ordinary differential equation

R. R. Gontsovab, I. V. Goryuchkinac

a Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow, Russia
b National Research University "Moscow Power Engineering Institute", Moscow, Russia
c Keldysh Institute of Applied Mathematics of Russian Academy of Sciences, Moscow, Russia

Abstract: A sufficient condition is proposed which ensures that a Dulac series that formally satisfies an algebraic ordinary differential equation (ODE) is convergent. Such formal solutions of algebraic ODEs are quite common: in particular, the Painlevé III, V and VI equations have formal solutions given by Dulac series; they are convergent in view of the sufficient condition presented.
Bibliography: 13 titles.

Keywords: algebraic ODE, formal solution, Dulac series, convergence.

Funding Agency Grant Number
Russian Science Foundation 18-41-05003
Russian Foundation for Basic Research 16-51-150005 НЦНИ_а
Russian Academy of Sciences - Federal Agency for Scientific Organizations PRAS-18-01
The research of R. R. Gontsov was carried out at Lomonosov Moscow State University with the support of the Russian Science Foundation under grant no. 18-41-05003. The research of I. V. Goryuchkina was carried out with the support of the Russian Foundation for Basic Research (grant no. 16-51-150005 НЦНИ_а) and also in the framework of the programme of the Presidium of the Russian Academy of Sciences no. 01 “Fundamental mathematics and its applications” (grant no. PRAS-18-01).

Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/sm9064

Full text: PDF file (640 kB)
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English version:
Sbornik: Mathematics, 2019, 210:9, 1207–1221

Bibliographic databases:

UDC: 517.927.7+517.922
MSC: Primary 34M45; Secondary 34A25
Received: 09.01.2018 and 28.01.2019

Citation: R. R. Gontsov, I. V. Goryuchkina, “Convergence of formal Dulac series satisfying an algebraic ordinary differential equation”, Mat. Sb., 210:9 (2019), 3–18; Sb. Math., 210:9 (2019), 1207–1221

Citation in format AMSBIB
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\pages 3--18
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\jour Sb. Math.
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\pages 1207--1221
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Gontsov R.R., Goryuchkina V I., “On the Convergence of Formal Exotic Series Solutions of An Ode”, Comput. Methods Funct. Theory  crossref  isi
  • Математический сборник Sbornik: Mathematics (from 1967)
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