On the stability problem for functional differential equations with infinite delay
type: Item
instance of: scholarly article
title: On the stability problem for functional differential equations with infinite delay
zbMATH Open document ID: 1189.34146
DOI: 10.3103/S1066369X08070049
author: S. V. Pavlikov
published in: Russian Mathematics
publication date: 2009-10-26T00:00:00Z
review text: The paper is devoted to the problem of stability of functional differential equations with infinite delay. The study is based on the limiting equations approach and Lyapunov's direct method. A theorem on localization of a positive limit set is established and four theorems on stability are stated in terms of Lyapunov functional of constant sign with a derivative of constant sign. The theorems are proved by using some results derived by \textit{N. O. Sedova} in [Differ. Equ. 38, No.~10, 1423--1434 (2002; Zbl 1036.34089)]. An illustrative example is given.
Mathematics Subject Classification ID: 34K20
zbMATH DE Number: 5621364
zbMATH Keywords: functional differential equations
zbMATH Keywords: infinite delay
zbMATH Keywords: Lyapunov functional of constant sign
zbMATH Keywords: limiting equations
reviewed by: Oleg Anashkin
MaRDI profile type: Publication
cites work: Q4163814
cites work: On the location of positive limit sets for autonomous functional differential equations with infinite delay
cites work: Q4740206
cites work: Q4236294
cites work: Q4201145
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description: scientific article; zbMATH DE number 5621364