A natural boundary for solutions to the second order pantograph equation
type: Item
instance of: scholarly article
title: A natural boundary for solutions to the second order pantograph equation
zbMATH Open document ID: 1066.34067
published in: Journal of Mathematical Analysis and Applications
publication date: 2005-01-12T00:00:00Z
review text: The authors study solutions to functional differential equations of the form \[ y(z)-ay'(z)-by(z)+\lambda y(az)=0, \] where \(\alpha,a\) and \(b\) are real constants such that \(\alpha>1\), \(a>0\), and \(b>0\). Here, \(z\) is a complex variable and \(\lambda\) is a nonzero parameter. They prove that if a solution \(y\) is holomorphic in some connected open subset of \(\{z\in\mathbb{C}: \text{Re}\,z>0\}\) whose boundary contains the imaginary axis and \(y\) has a singularity at \(z=0\), then \(y\) has the imaginary axis as its natural boundary.
reviewed by: Ludvík Janoš
Mathematics Subject Classification ID: 34K06
zbMATH DE Number: 2126891
author: Jonathan C. Marshall
author: B. Van Brunt
author: G. C. Wake
MaRDI profile type: Publication
full work available at URL: j.jmaa.2003.12.051
OpenAlex ID: W2044920957
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DOI: 10.1016/J.JMAA.2003.12.051
description: scientific article; zbMATH DE number 2126891