On the stability of some exponential polynomials
type: Item
instance of: scholarly article
title: On the stability of some exponential polynomials
zbMATH Open document ID: 0888.34063
published in: Journal of Mathematical Analysis and Applications
publication date: 1997-04-29T00:00:00Z
review text: The authors deal with the transcendental equation of the type \[ (z+ pz+ q)\exp(\tau z)+ rz=0, \] where \(p\), \(q\), \(r\), \(\mathbb{R}\), \(\tau, p>0\), \(q>0\), \(r=0\), \(n=0,1,2\). The main results are concerned with the case \(n=0\), which is important in the stability theory of delay. A new necessary and sufficient condition for all the roots to lie to the left of the imaginary axis is given. The proofs are elementary and independent of Pontryagin's results. Applying the same approach in the cases \(n=1\) and \(n=2\), the authors give sufficient conditions for instability.
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 34D05
zbMATH DE Number: 1005713
zbMATH Keywords: transcendental equation
zbMATH Keywords: stability theory
zbMATH Keywords: delay
author: Margarete Z. Baptistini
author: Plácido Zoega Táboas
reviewed by: Janusz Matkowski
MaRDI profile type: Publication
full work available at URL: jmaa.1996.5152
OpenAlex ID: W1969372401
cites work: On the existence and global bifurcation of periodic solutions to planar differential delay equations
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cites work: On the zeros of some transcendental functions
cites work: Periodic solutions of a planar delay equation
DOI: 10.1006/JMAA.1996.5152
description: scientific article; zbMATH DE number 1005713