Relations between solutions of differential equations and small functions
type: Item
instance of: scholarly article
title: Relations between solutions of differential equations and small functions
zbMATH Open document ID: 1242.30024
DOI: 10.1155/2012/358027
author: Zongxuan Chen
author: Wei Liu
published in: Abstract and Applied Analysis
publication date: 2012-05-14T00:00:00Z
Mathematics Subject Classification ID: 30D35
Mathematics Subject Classification ID: 34M05
zbMATH DE Number: 6034207
zbMATH Keywords: linear differential equation in \(\mathbb{C}\)
zbMATH Keywords: meromorphic solutions
zbMATH Keywords: Nevanlinna theory
zbMATH Keywords: fixed points
Wikidata QID: Q58696397
reviewed by: Zhibo Huang
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/358027
OpenAlex ID: W2074399957
cites work: On the characteristic of functions meromorphic in the unit disk and of their integrals
cites work: Q2996469
cites work: Q3104933
cites work: Q4514593
cites work: Relation between differential polynomials and small functions
cites work: Growth of solutions and oscillation of differential polynomials generated by some complex linear differential equations
cites work: Oscillation of solutions of linear differential equations
cites work: Q5291660
cites work: Fixed Points and Hyper Order of Differential Polynomials Generated by Solutions of Differential Equation
cites work: Q3071202
cites work: Q3148124
cites work: Streng converse inequality for the F operators
cites work: Estimates for the Logarithmic Derivative of a Meromorphic Function, Plus Similar Estimates
review text: In this paper, the authors use Nevanlinna theory and oscillation theory of meromorphic functions to study the higher order linear differential equations NEWLINE\[NEWLINE f^{(k)}+A_{k-1}(z)f^{(k-1)}+\dots+A_{1}(z)f'+A_{0}(z)f=0, NEWLINE\]NEWLINE where \(A_{k-1}(z),\dots,A_{1}(z)\) and \(A_{0}(z)\) are entire functions of finite order such that if \(A_{j}(z)\not\equiv 0\), then \(\lambda(A_{j})<\sigma(A_{j})\); if \(i\neq j\), then \(\sigma(A_{i}/A_{j})=\max\{\sigma(A_{i}), \sigma(A_{j})\}\). The authors derive some relations between the meromorphic solutions of such an equation and prove that every meromorphic solution and its derivative have infinitely many fixed points.
description: scientific article; zbMATH DE number 6034207