Interval oscillation criteria for nonlinear differential equations with impulses and variable delay
type: Item
instance of: scholarly article
title: Interval oscillation criteria for nonlinear differential equations with impulses and variable delay
zbMATH Open document ID: 1403.34051
author: Xiaoliang Zhou
author: Changdong Liu
author: Wu-Sheng Wang
published in: Applied Mathematics Letters
publication date: 2018-11-02T00:00:00Z
review text: This paper deals with the second order impulsive delay differential equation of the form \[ x^{\prime\prime}(t)+p(t)g(x(t-\tau (t))) =f(t),~t\geq t_{0},~t\neq \theta _{k}, \] \[ x(t^{+}) =a_{k}x(t),~x^{\prime }(t^{+})=b_{k}x^{\prime }(t_{k}),~t=\theta _{k},~k=1,2,\dots . \] First, strong zero point and weak zero point are defined. Then an estimation for the function \(x(t-\tau (t))/x(t)\) is obtained. Finally, using the Riccati transformation, some interval oscillation criteria are established.
reviewed by: Fatma Karakoç
Mathematics Subject Classification ID: 34K11
Mathematics Subject Classification ID: 34K45
zbMATH DE Number: 6971570
zbMATH Keywords: interval oscillation
zbMATH Keywords: impulse
zbMATH Keywords: variable delay
zbMATH Keywords: interval delay function
MaRDI profile type: Publication
full work available at URL: j.aml.2018.06.007
OpenAlex ID: W2808347368
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Wikidata QID: Q129656993
DOI: 10.1016/J.AML.2018.06.007
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description: scientific article; zbMATH DE number 6971570