New contributions to the related work of Paul Appell, Lazarus Fuchs, Georg Hamel, and Paul Painlevé on nonlinear differential equations whose solutions are free of movable branch points
type: Item
instance of: scholarly article
title: New contributions to the related work of Paul Appell, Lazarus Fuchs, Georg Hamel, and Paul Painlevé on nonlinear differential equations whose solutions are free of movable branch points
zbMATH Open document ID: 0619.34013
DOI: 10.1016/0022-0396(87)90187-2
author: Roger Chalkley
published in: Journal of Differential Equations
publication date: 1987-01-01T00:00:00Z
review text: A second order algebraic differential equation of degree n is given by an equation of the form \(\Phi (z,y,y',y'')=0,\) where \(\Phi\) is a polynomial with meromorphic coefficients. This paper is concerned with the problem whether the solutions of this equation are free of movable critical points. If \(\Phi\) is linear in y'', much is known about it; the author here presents what appears to be the only interesting results known for equations of higher degree in y''. Some of the results are based on findings by the French nineteenth-century mathematician Paul Appell.
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 4004640
zbMATH Keywords: second order algebraic differential equation
zbMATH Keywords: meromorphic coefficients
zbMATH Keywords: movable critical points
MaRDI profile type: Publication
full work available at URL: 0022-0396(87)90187-2
OpenAlex ID: W1967427183
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description: scientific article; zbMATH DE number 4004640