An extension of the Alekseev variation of constant formula for neutral nonlinear perturbed equation with an application to the relative asymptotic equivalence
type: Item
instance of: scholarly article
title: An extension of the Alekseev variation of constant formula for neutral nonlinear perturbed equation with an application to the relative asymptotic equivalence
zbMATH Open document ID: 0615.34069
DOI: 10.1016/0022-247X(87)90341-6
author: Yanyan Li
published in: Journal of Mathematical Analysis and Applications
publication date: 1987-01-01T00:00:00Z
review text: The authors consider nonlinear neutral functional differential equations and certain perturbations of these and the relative asymptotic equivalence between solutions. Sufficient conditions, using an Alekseev- type variation of constants formula, are given for such relative asymptotic equivalence. This paper contains rather detailed technicalities and assumes a fair amount of familiarity with neutral functional equation theory and notation. The reviewer also noted a number of inconsistences in it; for example, in the definition of D(t,\(\phi)\), it seems the lower limit of integration should be \(\sigma\)-r rather than -r; also in the remark following Lemma 2.1, D(t,\(\phi)\) seems to be assumed independent of t; in fact, this is the case in the example discussed in the last section of this paper.
reviewed by: G.Seifert
Mathematics Subject Classification ID: 34K20
zbMATH DE Number: 3996189
zbMATH Keywords: nonlinear neutral functional differential equations
zbMATH Keywords: perturbations
zbMATH Keywords: Alekseev-type variation of constants formula
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3996189