Growth properties for solutions of differential equations defined in the disk
type: Item
instance of: scholarly article
title: Growth properties for solutions of differential equations defined in the disk
zbMATH Open document ID: 0769.30018
DOI: 10.1007/BF01760009
author: Linda R. Sons
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 1993-05-16T00:00:00Z
review text: Let \(F\) be the class of meromorphic functions \(f\) in the unit disk \(D\) for which the Nevanlinna characteristic has a slow growth in the sense that \(\limsup_{r\to 1} T(r,f)/(-\log(1-r))=\alpha(f)<\infty\). This paper is devoted to consider the growth of solutions \(y_ 0\), such that \(\lim_{r\to 1} T(r,y_ 0)=+\infty\), of generalized algebraic differential equations of the form \(\sum_{\alpha\in I} f_ \alpha(z) y^{\alpha_ 0}(y')^{\alpha_ 1}\dots (y^{(k)})^{\alpha_ k}=0\) with coefficients \(f_ \alpha=f_{\alpha_ 0,\alpha_ 1,\dots, \alpha_ k}\) in the class \(F\). The results are too technical to be repeated here. Essentially, the idea is to find out additional assumptions which imply that \(y_ 0\in F\), too. For a related earlier paper, see \textit{S. Bank} [Ann. Mat. Pura Appl., IV. Ser. 92, 323-335 (1992; Zbl 0246.34004)].
reviewed by: Ilpo Laine
Mathematics Subject Classification ID: 30D35
Mathematics Subject Classification ID: 34M99
zbMATH DE Number: 169841
zbMATH Keywords: Nevanlinna characteristic
MaRDI profile type: Publication
cites work: Q5658395
cites work: On solutions of algebraic differential equations whose coefficients are analytic functions in the unit disk
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cites work: Q5723337
cites work: Boundary behaviour and normal meromorphic functions
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full work available at URL: https://doi.org/10.1007/bf01760009
OpenAlex ID: W1992471428
description: scientific article; zbMATH DE number 169841