On Picard's theorem
type: Item
instance of: scholarly article
title: On Picard's theorem
zbMATH Open document ID: 1386.34141
author: Bao Qin Li
published in: Journal of Mathematical Analysis and Applications
publication date: 2018-02-13T00:00:00Z
review text: In this paper, the author gives a connection/equivalence between Picard's theorem and the characterization of entire solutions of a differential equation. He proved that let \(a(z)\) be an entire function and let \(P(z)\) be a meromorphic function in \(\mathbb C\) with at least two distinct zeros, then an entire solution of the differential equation \[ f'+a(z)P(f)=0 \] must be constant. He also proves that this result and Picard's Theorem are equivalent in the sense that one implies the other.
Mathematics Subject Classification ID: 34M05
Mathematics Subject Classification ID: 30D30
zbMATH DE Number: 6837568
zbMATH Keywords: Picard's theorem
zbMATH Keywords: differential equation
zbMATH Keywords: entire function
zbMATH Keywords: meromorphic function
reviewed by: Liangwen Liao
MaRDI profile type: Publication
full work available at URL: j.jmaa.2017.12.010
OpenAlex ID: W2771213051
cites work: Q5179675
cites work: Picard's Theorem and Brownian Motion
cites work: Q5537833
cites work: Q5723337
cites work: Picard's Theorem and Rickman's Theorem by Way of Harnack's Inequality
cites work: Estimates on derivatives and logarithmic derivatives of holomorphic functions and Picard's theorem
cites work: A logarithmic derivative lemma in several complex variables and its applications
cites work: An Equivalent Form of Picard’s Theorem and Beyond
cites work: Q3940060
cites work: The lemma of the logarithmic derivative in several complex variables
cites work: CURVES, DOMAINS AND PICARD'S THEOREM
DOI: 10.1016/J.JMAA.2017.12.010
description: scientific article; zbMATH DE number 6837568