A. O. Remizov, “Singularities of quasi-linear differential equations”, Dal'nevost. Mat. Zh., 23:1 (2023), 85

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Dal'nevostochnyi Matematicheskii Zhurnal, 2023, Volume 23, Number 1, Pages 85–105
DOI: https://doi.org/10.47910/FEMJ202308 (Mi dvmg509)

Singularities of quasi-linear differential equations

A. O. Remizov

Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow region

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DOI: https://doi.org/10.47910/FEMJ202308

Abstract: We study solutions of quasi-linear ordinary differential equations of the second order at their singular points, where the coefficient of the second-order derivative vanishes. Either solutions entering a singular point with definite tangential direction (proper solutions) or those without definite tangential direction (oscillating solutions) are considered. It is shown that oscillating solutions generically do not exist, and proper solutions enter a singular point in strictly definite tangential directions. A local representation for proper solutions in a form similar to Newton–Puiseux series is obtained.

Key words: singular points, normal forms, resonances, invariant manifolds, oscillating solutions.

Funding agency	Grant number
Ministry of Science and Higher Education of the Russian Federation	075-00337-20-03 0714-2020-0005
Russian Foundation for Basic Research	20-01-00610
The work was supported financially by the Ministry of Science and Higher Education of the Russian Federation (state task 075-00337-20-03, project 0714-2020-0005) and the Russian Foundation for Basic Research (grant 20-01-00610).

Received: 18.07.2022

Document Type: Article

UDC: 517.9

MSC: Primary 34A12; Secondary 34C05

Language: Russian

Citation: A. O. Remizov, “Singularities of quasi-linear differential equations”, Dal'nevost. Mat. Zh., 23:1 (2023), 85–105

Citation in format AMSBIB

\Bibitem{Rem23}

\by A.~O.~Remizov

\paper Singularities of quasi-linear differential equations

\jour Dal'nevost. Mat. Zh.

\yr 2023

\vol 23

\issue 1

\pages 85--105

\mathnet{http://mi.mathnet.ru/dvmg509}

\crossref{https://doi.org/10.47910/FEMJ202308}

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