On the growth of meromorphic solutions of some algebraic differential equations
type: Item
instance of: scholarly article
title: On the growth of meromorphic solutions of some algebraic differential equations
zbMATH Open document ID: 0628.34007
author: Nobushige Toda
published in: Tôhoku Mathematical Journal. Second Series
publication date: 1986-01-01T00:00:00Z
review text: Let X, Y, a, \(a_{ij}\) be meromorphic functions satisfying \[ X^ n=aY^ m+\sum^{k}_{\nu =0}\sum_{i+j=\nu}a_{ij}X^ iY^ j,\quad XY\neq 0 \] and \(X^ n\neq aY^ m\). If \(n\geq m>k+2+m/n\), then \(T(r,X)=O(\sum T(r,a_{ij})+T(r,a))+S(r,X),\) \(r\to \infty\). This theorem has interesting applications to the meromorphic solutions of the differential equation \[ (w^{(m)})^ n+Q_{n-1}(w,z)(w^{(m)})^{n- 1}+...+Q_ 0(w,z)=0 \] with meromorphic coefficients.
Mathematics Subject Classification ID: 34M05
Mathematics Subject Classification ID: 30D35
Mathematics Subject Classification ID: 30D05
zbMATH DE Number: 4021621
zbMATH Keywords: meromorphic solutions
zbMATH Keywords: meromorphic coefficients
reviewed by: Alexandre Eremenko
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1178228412
OpenAlex ID: W1993477601
cites work: Meromorphic solutions of algebraic differential equations
cites work: Zur Theorie der gewohnlichen Differentialgleichungen im Komplexen
cites work: Q3658242
cites work: Q5723337
cites work: Estimates for the Nevanlinna characteristics of some classes of meromorphic functions and their applications to differential equations
cites work: On a conjecture of Gackstatter and Laine
cites work: Q3852477
cites work: On the conjecture of Gackstatter and Laine concerning the differential equation \((w')^ n=\sum^{m}_{j=0}a_ j(z)w^ j\)
cites work: On the growth of meromorphic solutions of an algebraic differential equation
cites work: On the growth of non-admissible solutions of the differential equation \((w')^ n=\sum ^{m}_{j=0}a_ jw^ j\)
DOI: 10.2748/TMJ/1178228412
description: scientific article; zbMATH DE number 4021621