Meromorphic solutions of first-order algebraic differential equations
type: Item
instance of: scholarly article
title: Meromorphic solutions of first-order algebraic differential equations
zbMATH Open document ID: 0656.34002
DOI: 10.1007/BF01086167
publication date: 1984-01-01T00:00:00Z
review text: Let K be the field of germs of meromorphic functions at \(\infty\), M be the field of functions which are meromorphic for \(r<| z| <\infty\) (r depends on the function). By \(K[t_ 1,...,t_ n]\), \(K(t_ 1,...,t_ n)\), respectively, we denote the ring of polynomials and field of rational functions in \(t_ 1,...,t_ n\) over K. Let \(y\in M\) be a solution of the differential equation \(F(y',y)=0\), \(F\in K[t_ 1,t_ 2]\). We study the order of the function y, i.e., the order of growth of the Nevanlinna characteristic T(r,y) as \(r\to \infty\).
Mathematics Subject Classification ID: 34M05
zbMATH DE Number: 4071345
zbMATH Keywords: meromorphic functions
author: Alexandre Eremenko
MaRDI profile type: Publication
cites work: On the growth of meromorphic solutions of the differential equation \((y')^m=R(z,y)\)
cites work: Q5797273
cites work: Eindeutige Lösungen der Differentialgleichung \(w'=R(z,w)\)
cites work: First order algebraic differential equations. A differential algebraic approach
published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 4071345