电邮这篇文章 Convergence of formal Dulac series satisfying an algebraic ordinary differential equation
- 作者: Gontsov R.R.1,2, Goryuchkina I.V.3
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隶属关系:
- Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute)
- National Research University "Moscow Power Engineering Institute"
- Keldysh Institute of Applied Mathematics of Russian Academy of Sciences
- 期: 卷 210, 编号 9 (2019)
- 页面: 3-18
- 栏目: Articles
- URL: https://journal-vniispk.ru/0368-8666/article/view/133280
- DOI: https://doi.org/10.4213/sm9064
- ID: 133280
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详细
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 Painleve 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.
作者简介
Renat Gontsov
Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute); National Research University "Moscow Power Engineering Institute"
Email: gontsovrr@gmail.com
Candidate of physico-mathematical sciences, Associate professor
Irina Goryuchkina
Keldysh Institute of Applied Mathematics of Russian Academy of Sciences
Email: igoryuchkina@gmail.com
Candidate of physico-mathematical sciences, Senior Researcher
参考
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- B. Malgrange, “Sur le theorème de Maillet”, Asymptot. Anal., 2:1 (1989), 1–4
- R. R. Gontsov, I. V. Goryuchkina, “On the convergence of generalized power series satisfying an algebraic ODE”, Asymptot. Anal., 93:4 (2015), 311–325
- J. Cano, “On the series defined by differential equations, with an extension of the Puiseux polygon construction to these equations”, Analysis, 13:1-2 (1993), 103–119
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