Exponential ordering for neutral functional differential equations with non-autonomous linear \(D\)-operator
type: Item
instance of: scholarly article
title: Exponential ordering for neutral functional differential equations with non-autonomous linear \(D\)-operator
zbMATH Open document ID: 1237.37022
author: Rafael Obaya
author: Víctor M. Villarragut
published in: Journal of Dynamics and Differential Equations
publication date: 2011-11-25T00:00:00Z
review text: This interesting paper investigates neutral functional differential equations with a stable linear time-dependent \(D\)-operator. Moreover, the operator of convolution \(\widehat{D}\) leaves the space of bounded uniformly continuous mappings in \(C((-\infty,0],{\mathbb R}^n)\) invariant. It is shown that if \(D\) is stable then \(\widehat{D}\) is invertible and, moreover, both \(\widehat{D}\) and \(\widehat{D}^{-1}\) are uniformly continuous in the compact-open topology on bounded sets. A new transformed exponential order is introduced and, under ambient assumptions, the authors derive a \(1\)-covering property for minimal sets. These results are applied to a class of extensively studied compartmental systems yielding information on the amount of material.
Mathematics Subject Classification ID: 37B55
Mathematics Subject Classification ID: 34K40
Mathematics Subject Classification ID: 34K14
zbMATH DE Number: 5980366
zbMATH Keywords: non-autonomous dynamical systems
zbMATH Keywords: monotone skew-product semiflows
zbMATH Keywords: neutral functional differential equations
zbMATH Keywords: infinite delay
zbMATH Keywords: compartmental systems
reviewed by: Christian Pötzsche
MaRDI profile type: Publication
full work available at URL: s10884-011-9210-9
OpenAlex ID: W1979777594
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DOI: 10.1007/S10884-011-9210-9
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description: scientific article; zbMATH DE number 5980366