On the convergence of generalized power series satisfying an algebraic ODE

Article type: Research Article

Authors: Gontsov, R.R.^{a; *} | Goryuchkina, I.V.^b

Affiliations: [a] Institute for Information Transmission Problems of the Russian Academy of Sciences, Moscow, Russia. E-mail: gontsovrr@gmail.com | [b] Keldysh Institute of Applied Mathematics of the Russian Academy of Sciences, Moscow, Russia. E-mail: igoryuchkina@gmail.com

Correspondence: [*] Corresponding author: R.R. Gontsov, Institute for Information Transmission Problems of the Russian Academy of Sciences, Bolshoy Karetny per. 19, Moscow, 127994, Russia. Tel.: +7 925 375 2008; Fax: +7 495 650 0579; E-mail: gontsovrr@gmail.com.

Abstract: Here we propose a sufficient condition of the convergence of a generalized power series formally satisfying an algebraic (polynomial) ordinary differential equation. The proof is based on the majorant method.

Keywords: algebraic ODE, formal solution, generalized power series, majorant method, convergent series

DOI: 10.3233/ASY-151297

Journal: Asymptotic Analysis, vol. 93, no. 4, pp. 311-325, 2015