On the convergence of generalized power series satisfying an algebraic ODE

DOI10.3233/ASY-151297zbMath1327.34014arXiv1407.1330OpenAlexW2964342807MaRDI QIDQ3195307

Renat Gontsov, Irina Goryuchkina

Publication date: 16 October 2015

Published in: Asymptotic Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1407.1330

zbMATH Keywords

majorant methodformal solutionconvergent seriesgeneralized power seriesalgebraic ODE

Mathematics Subject Classification ID

Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. (34A25) Formal solutions and transform techniques for ordinary differential equations in the complex domain (34M25)

Related Items (7)

On the convergence of generalized power series solutions of \(q\)-difference equations ⋮ Liouvillian integrability and the Poincaré problem for nonlinear oscillators with quadratic damping and polynomial forces ⋮ Asymptotic integration of the Riccati equation by methods of power geometry ⋮ On the convergence of formal exotic series solutions of an ODE ⋮ The Maillet-Malgrange type theorem for generalized power series ⋮ Towards the Convergence of Generalized Power Series Solutions of Algebraic ODEs ⋮ Convergence of formal Dulac series satisfying an algebraic ordinary differential equation

Cites Work

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• ON THE SERIES DEFINED BY DIFFERENTIAL EQUATIONS, WITH AN EXTENSION OF THE PUISEUX POLYGON CONSTRUCTION TO THESE EQUATIONS
• Asymptotic behaviour and expansions of solutions of an ordinary differential equation

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