Sur les équations différentielles du second ordre et du premier degré dont l'intégrale générale est a points critiques fixes

1910/01/01 by B. Gambier, Bertrand Gambier · 540 citations
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Humanities #Mathematics #Numerical methods for differential equations #Philosophy

paper · pdf · doi:10.1007/bf02393211

published in Acta Mathematica 33(0), 1-55 (Mittag-Leffler Institute)

openalex publication_date 1910/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Introduction.1. --Objet de ce mdmoire.--M.PAINLEV~ a indiqu~ une m6thode pour d6terminer routes ]es 6quations diff~rentielles (alg~briques) du second ordre dont les points critiques sont fixes et il a d~velopp~ eette methode explicitement dans le cas eh l'6quation est de ia formeR rationnel en yr, alg6brique en y, alg~brique ou analytique en x.Un m6moire publi~ dans les Acta Mathematiea (1902) renferme le tableau de routes les ~quations (i) ~ points critiques fixes.Ayant commence, sur les conseils de M. PAI:NLEVE, l'application de sa m6thode aux ~quations qui sont non plus du premier degrd mais du second en y', j'ai ~t6 conduit s r6viser l'~num6ration des 6quations (i) et j'ai constat6 que les tableaux dresses par M. PA~NLEVE pr6sentaient une lacune que je comblerai dans le pr6sent m6moire.Cette lacune provient de ce que dans la discussion des cas nombreux que la m6thode conduit ~ distinguer, M. PAISLEV~.en a laiss6 6chapper un, qui se trouve correspondre ~ des types nombreux et importants.Je pr~,ciserai d'abord cette omission.

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