On the 3/2 stability theorem for one-dimensional delay-differential equations
type: Item
instance of: scholarly article
title: On the 3/2 stability theorem for one-dimensional delay-differential equations
zbMATH Open document ID: 0655.34062
DOI: 10.1016/0022-247X(87)90171-5
author: T. Yoneyama
published in: Journal of Mathematical Analysis and Applications
publication date: 1987-01-01T00:00:00Z
review text: Consider the one-dimensional delay-differential equation (1) \(\dot x(t)=- a(t)x(t-\gamma (t))\) where a: [0,\(\infty)\to [0,\infty)\) and \(r: [0,\infty)\to [0,q].\) \textit{J. C. Lillo} [J. Differ. Equations 6, 1-35 (1969; Zbl 0174.398)] proved that if there is \(\alpha >0\) such that a(t)\(\leq \alpha\) and \(\alpha\) \(q\leq 3/2\), then the zero solution of (1) is uniformly stable. Furthermore, the upper bound 3/2 is the best possible for (1). In this paper the author considers such a problem for more general one-dimensional delay-differential equation than (1): (2) \(\dot x(t)=F(t,x_ t)\). He obtains some results on the uniform stability of the zero solution of (2).
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 34D20
zbMATH DE Number: 4069388
zbMATH Keywords: delay-differential equation
zbMATH Keywords: uniform stability
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4069388