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
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.
algebraic ODE, formal solution, Dulac series, convergence.
|Russian Science Foundation
|Russian Foundation for Basic Research
|Russian Academy of Sciences - Federal Agency for Scientific Organizations
|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).
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Sbornik: Mathematics, 2019, 210:9, 1207–1221
MSC: Primary 34M45; Secondary 34A25
Received: 09.01.2018 and 28.01.2019
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
\by R.~R.~Gontsov, I.~V.~Goryuchkina
\paper Convergence of formal Dulac series satisfying an algebraic ordinary differential equation
\jour Mat. Sb.
\jour Sb. Math.
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This publication is cited in the following articles:
Gontsov R.R., Goryuchkina V I., “On the Convergence of Formal Exotic Series Solutions of An Ode”, Comput. Methods Funct. Theory
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