Generic oscillations of delay differential system with impulses.
type: Item
instance of: scholarly article
title: Generic oscillations of delay differential system with impulses.
zbMATH Open document ID: 1046.34084
DOI: 10.1016/S0898-1221(03)00021-X
author: Yongrui Duan
author: Peng Tian
author: Weiping Zhang
author: Wei Feng
publication date: 2003-12-14T00:00:00Z
review text: The authors consider the linear functional system \[ X^{\prime}(t)+AX(t)+BX(t-\tau )=0,\quad t\geq t_{0},\;t\neq t_{k},\tag{*} \] with the linear impulsive condition \[ X(t_{k}^{+})-X(t_{k})=C_{k}X(t_{k}),\quad k=1,2,\dots \tag{**} \] They compare the oscillation and nonoscillation of the impulsive systems (*) and (**) with nonimpulsive systems which recently have been used by some authors especially in the oscillation of nonlinear delay impulsive differential equations. By using properties of the characteristic equation, they establish some explicit sufficient conditions for generic oscillations and for generic nonoscillations. The definitions of the generic oscillation and generic nonoscillation are also included.
Mathematics Subject Classification ID: 34K11
Mathematics Subject Classification ID: 34K06
Mathematics Subject Classification ID: 34K45
zbMATH DE Number: 2017212
zbMATH Keywords: generic oscillation
zbMATH Keywords: impulsive delay differential systems
reviewed by: S. H. Saker
MaRDI profile type: Publication
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full work available at URL: s0898-1221(03)00021-x
OpenAlex ID: W1985411080
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published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 2017212