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Movable Singular Points of Polynomial Ordinary Differential Equations

Movable Singular Points of Polynomial Ordinary Differential Equations Differential Equations, Vol. 40, No. 6, 2004, pp. 807–814. Translated from Differentsial'nye Uravneniya, Vol. 40, No. 6, 2004, pp. 756–762. Original Russian Text Copyright c 2004 by Sobolevskii. ORDINARY DIFFERENTIAL EQUATIONS Movable Singular Points of Polynomial Ordinary Di erential Equations S. L. Sobolevskii Belarus State University, Minsk, Belarus Received April 17, 2001 INTRODUCTION Movable singular points of polynomial ordinary di erential equations of the form (n) (n1) (n2) w = P w ;w ;:::;w;z ; (1) where n is a positive integer, z is an independent complex variable, w is a complex-valued function of z,and P is a polynomial in w and its derivatives with coecients analytic with respect to z in some domain U of the complex plane, were studied in a number of papers. Concerning the absence of movable critical singular points, the complete classi cation of polynomial di erential equations of order  4 is known. The classi cation of rst- and second-order equations follows from the classi cation of rst-order algebraic equations (see related references in [1]) and second-order rational equations [2], respectively. A complete classi cation was given for third-order polynomial equations in [3{5] and for fourth-order polynomial equations in [6{8]. Some isolated results http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

Movable Singular Points of Polynomial Ordinary Differential Equations

Sobolevskii, S.
Differential Equations , Volume 40 (6) – Nov 14, 2004
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References (7)

Publisher
Springer Journals
Copyright
Copyright © 2004 by MAIK “Nauka/Interperiodica”
Subject
Mathematics; Difference and Functional Equations; Ordinary Differential Equations; Partial Differential Equations
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1023/B:DIEQ.0000046859.46244.5e
Publisher site
See Article on Publisher Site

Abstract

Differential Equations, Vol. 40, No. 6, 2004, pp. 807–814. Translated from Differentsial'nye Uravneniya, Vol. 40, No. 6, 2004, pp. 756–762. Original Russian Text Copyright c 2004 by Sobolevskii. ORDINARY DIFFERENTIAL EQUATIONS Movable Singular Points of Polynomial Ordinary Di erential Equations S. L. Sobolevskii Belarus State University, Minsk, Belarus Received April 17, 2001 INTRODUCTION Movable singular points of polynomial ordinary di erential equations of the form (n) (n1) (n2) w = P w ;w ;:::;w;z ; (1) where n is a positive integer, z is an independent complex variable, w is a complex-valued function of z,and P is a polynomial in w and its derivatives with coecients analytic with respect to z in some domain U of the complex plane, were studied in a number of papers. Concerning the absence of movable critical singular points, the complete classi cation of polynomial di erential equations of order  4 is known. The classi cation of rst- and second-order equations follows from the classi cation of rst-order algebraic equations (see related references in [1]) and second-order rational equations [2], respectively. A complete classi cation was given for third-order polynomial equations in [3{5] and for fourth-order polynomial equations in [6{8]. Some isolated results

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Differential Equations – Springer Journals

Published: Nov 14, 2004

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