Exponential dichotomy and stability of neutral type equations
type: Item
instance of: scholarly article
title: Exponential dichotomy and stability of neutral type equations
zbMATH Open document ID: 0664.34073
DOI: 10.1016/0022-0396(88)90061-7
author: V. G. Kurbatov
author: R. R. Akhmerov
published in: Journal of Differential Equations
publication date: 1988-01-01T00:00:00Z
review text: The authors study the linear functional differential equation of neutral type with unbounded delay (1) \(Lx=(d/ds)Dx+Bx=0\) where D, B are linear bounded retarded operators with exponentially fading memory. If L is understood as an operator from C into the special space \(C^{-1}\) of distributions, then its invertibility is equivalent to the presence of exponential dichotomy of the solutions of (1). The theory is applied to prove theorems on stability and instability in the first approximation for neutral functional differential equations of a general form.
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 34D20
zbMATH DE Number: 4086131
zbMATH Keywords: linear functional differential equation of neutral type with unbounded delay
zbMATH Keywords: exponentially fading memory
zbMATH Keywords: neutral functional differential equations
reviewed by: Alan R. Hausrath
MaRDI profile type: Publication
full work available at URL: 0022-0396(88)90061-7
OpenAlex ID: W2084723043
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description: scientific article; zbMATH DE number 4086131