A variation of constants formula for an abstract functional differential equation of retarded type
type: Item
instance of: scholarly article
title: A variation of constants formula for an abstract functional differential equation of retarded type
zbMATH Open document ID: 0879.34072
published in: Differential and Integral Equations
publication date: 1997-12-10T00:00:00Z
review text: The authors derive a variation of parameters formula for the equation \(x'(t)=L(x_t)+f(t)\), where \(L:C([-r,0],E)\to E\) is a bounded linear operator, \(E\) is a Banach space and \(x_t(\theta)=x(t+\theta), \theta \in [-r,0]\). They use a decomposition of the space \(C([-r,0],E)\) with respect to the spectrum of a generator of a solution semigroup for the homogeneous problem to obtain a decomposition of the solution and corresponding projectors.
Mathematics Subject Classification ID: 34K30
Mathematics Subject Classification ID: 47D06
zbMATH DE Number: 1095815
zbMATH Keywords: functional differential equation
zbMATH Keywords: variation of parameters formula
zbMATH Keywords: fundamental solution
zbMATH Keywords: spectral decomposition
author: Ovide Arino
author: Eva Sánchez
reviewed by: Hana Petzeltová
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1095815