Algebraic differential equations of the first order free from parametric singularities from the differential-algebraic standpoint

Michihiko MATSUDA

doi:10.2969/jmsj/03030447

Michihiko MATSUDA

著者情報

ジャーナルフリー

1978 年 30 巻 3 号 p. 447-455

DOI https://doi.org/10.2969/jmsj/03030447

詳細

Published: 1978 Received: 1976/10/18 Available on J-STAGE: 2006/10/20 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/10/20 訂正理由: - 訂正箇所: 論文抄録訂正内容: Right : A differential-algebraic definition for an algebraic differential equation of the first order to be free from parametric singularities will be given. From this standpoint we shall prove three theorems which are essentially due to Briot and Bouquet, Fuchs, and Poincaré respectively.

訂正日: 2006/10/20 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Right : [1] A. R. Forsyth, Theory of differential equations, Part II, Ordinary equations, not linear, II Cambridge Univ. Press, London, 1906.
[2] L. Fuchs, Über Differentialgleichungen, deren Integrale feste Verzweigungspunkte besitzen, S.-B. der Königl. preussischen Akad. Wiss. Berlin, 32 (1884), 699-710.
[3] E. R. Kolchin, Galois theory of differential fields, Amer. J. Math., 75 (1953), 753-824.
[4] P. Painlevé, Mémoire sur les équations différentielles du premier ordre, Ann. Sci. Ecole Norm. Sup., 3^e Série 8 (1891), 9-58, 103-140, 201-226, 267-284; 9 (1892), 9-30, 101-144, 283-308.
[5] P. Painlevé, Leçons sur la théorie analytique des équations différentielles, professées à Stockholm (1895), Hermann, Paris, 1897; OEuvres, Tome I, 205-798, Centre National de la Recherche Scientifique, Paris, 1972.
[6] É. Picard, Traité d'analyse, Tome III, 2^e Édition, Gauthier-Villars, Paris, 1908.
[7] H. Poincaré, Sur un théorème de M. Fuchs, Acta Math., 7 (1885), 1-32.
[8] M. Rosenlicht, On the explicit solvability of certain transcendental equations, Inst. Hautes Études Sci. Publ. Math., no. 36 (1969), 15-22.
[9] M. Rosenlicht, An analogue of L'Hospital's rule, Proc. Amer. Math. Soc., 37 (1973), 369-373.
[10] H. Weber, Lehrbuch der Algebra, Band III, 2. Aufl., Druck und Verlag von Friedr, Vieweg & Sohn Akt.-Ges., Braunschweig, 1908.

訂正日: 2006/10/20 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

抄録

A differential-algebraic definition for an algebraic differential equation of the first order to be free from parametric singularities will be given. From this standpoint we shall prove three theorems which are essentially due to Briot and Bouquet, Fuchs, and Poincaré respectively.

責任著者(Corresponding author)

訂正情報

J-STAGEへの登録はこちら（無料）