V. A. Belsky, V. I. Mironenko, “Constructing of Abel equations quivalented to the equation of the form $\dot{x}=A(t)(\xi_{0}+\xi_{1}x+\xi_{2}x^2+\xi

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Problemy Fiziki, Matematiki i Tekhniki (Problems of Physics, Mathematics and Technics), 2012, Issue 2(11), Pages 55–61 (Mi pfmt24)

This article is cited in 2 scientific papers (total in 2 papers)

MATHEMATICS

Constructing of Abel equations quivalented to the equation of the form

$\dot{x}=A(t)(\xi_{0}+\xi_{1}x+\xi_{2}x^2+\xi_{3}x^3)$

V. A. Belsky^a, V. I. Mironenko^b

^a Gomel Engineering Institute of the Ministry for Emergency Situations of the Republic of Belarus, Gomel
^b F. Scorina Gomel State University, Gomel

Full-text PDF (369 kB) Citations (2)

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Abstract: The sufficient conditions for coinsidering Mironenko reflecting functions of Abel equations

$\dot{x}= a_0 (t) + a_1 (t)x + a_2 (t)x^2 + a_3 (t)x^3$ and

$\dot{x}=A(t)(\xi_{0}+\xi_{1}x+\xi_{2}x^2+\xi_{3}x^3)$ where

$\xi_i$ are constants are established. Obtained results are illustrated by examples.

Keywords: Abel equation, reflecting function, equivalence of differential equations, polynomial perturbations.

Received: 06.01.2012

Document Type: Article

UDC: 517.925

Language: Russian

Citation: V. A. Belsky, V. I. Mironenko, “Constructing of Abel equations quivalented to the equation of the form

$\dot{x}=A(t)(\xi_{0}+\xi_{1}x+\xi_{2}x^2+\xi_{3}x^3)$ ”, PFMT, 2012, no. 2(11), 55–61

Citation in format AMSBIB

\Bibitem{BelMir12}

\by V.~A.~Belsky, V.~I.~Mironenko

\paper Constructing of Abel equations quivalented to the equation of the form $\dot{x}=A(t)(\xi_{0}+\xi_{1}x+\xi_{2}x^2+\xi_{3}x^3)$

\jour PFMT

\yr 2012

\issue 2(11)

\pages 55--61

\mathnet{http://mi.mathnet.ru/pfmt24}

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https://www.mathnet.ru/eng/pfmt24

https://www.mathnet.ru/eng/pfmt/y2012/i2/p55

This publication is cited in the following 2 articles:

M. S. Belokurskii, “Pochti periodicheskie resheniya pochti periodicheskogo uravneniya Abelya s lineinoi otrazhayuschei funktsiei”, PFMT, 2020, no. 4(45), 88–90
V. I. Mironenko, “O periodicheskikh resheniyakh uravneniya Rikkati”, PFMT, 2015, no. 2(23), 62–64

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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References:	36

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