R. R. Gontsov, I. V. Goryuchkina, “Convergence of formal Dulac series satisfying an algebraic ordinary differential equation”, Mat. Sb., 2019, Volume 210, Number 9,Pages <nobr>3

This article is cited in 5 papers

Convergence of formal Dulac series satisfying an algebraic ordinary differential equation

R. R. Gontsov^ab, I. V. Goryuchkina^c

^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.

UDC: 517.927.7+517.922

MSC: Primary 34M45; Secondary 34A25

Received: 09.01.2018 and 28.01.2019

DOI: 10.4213/sm9064