Inequalities and stability for a linear scalar functional differential equation
type: Item
instance of: scholarly article
title: Inequalities and stability for a linear scalar functional differential equation
zbMATH Open document ID: 1064.34062
author: Tingxiu Wang
published in: Journal of Mathematical Analysis and Applications
publication date: 2004-11-23T00:00:00Z
review text: The paper is concerned with the stability of the zero solution for the nonautonomous linear scalar functional-differential equation with one fixed delay \[ x'(t) = a(t)x(t) + b(t)x(t-h) \quad\text{for }t > t_0, \] addressing the cases where \(a(t)\) may have variable sign or \(b(t)\) may be unbounded. A typical result, assuming \(h = 1\) without loss of generality, implies that \[ | x(t)| = O\Biggl(\exp\biggl(\frac{1}{2}\int_{t_0}^{t-1/2} (a(s) + b(s+1)) \,ds\biggr)\Biggr), \] if \(-1/2 \leq a(t) + b(t+1) \leq -b^2(t+1)\) for all \(t\). Lower bounds are also derived. The proofs use Lyapunov functionals.
reviewed by: Hans Engler
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 34K06
Mathematics Subject Classification ID: 34K12
zbMATH DE Number: 2117725
zbMATH Keywords: functional-differential equation
zbMATH Keywords: stability
zbMATH Keywords: Lyapunov functional
MaRDI profile type: Publication
full work available at URL: j.jmaa.2004.01.048
OpenAlex ID: W2090537520
Wikidata QID: Q115346365
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DOI: 10.1016/J.JMAA.2004.01.048
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description: scientific article; zbMATH DE number 2117725