Necessary and sufficient conditions for oscillation of solutions to second-order neutral differential equations with impulses
type: Item
instance of: scholarly article
title: Necessary and sufficient conditions for oscillation of solutions to second-order neutral differential equations with impulses
zbMATH Open document ID: 1492.34070
author: S. S. Santra
published in: Tatra Mountains Mathematical Publications
publication date: 2021-12-06T00:00:00Z
review text: \noindent This paper deals with an impulsive neutral differential equation of the form \[ \left \{ \begin{array}{c} \left( r(t)(z^{\prime }(t))^{\gamma }\right) ^{\prime }+q(t)x^{\alpha }(\sigma (t))=0,~t\geq t_{0},~t\neq \lambda _{k}, \\ \Delta (r(\lambda _{k})(z^{\prime }(\lambda _{k}))^{\gamma })+h(\lambda _{k})x^{\alpha }(\sigma (\lambda _{k}))=0,~k\in \mathbb{N}, \end{array} \right. \] where \(z(t)=x(t)+x(\tau (t)).~\)Necessary and sufficient conditions are obtained for the oscillation of the solutions for the cases \(\gamma >\alpha \) and \(\gamma <\alpha .\) Moreover, two examples are given to illustrate the main results.
reviewed by: Fatma Karakoç
Mathematics Subject Classification ID: 34K11
Mathematics Subject Classification ID: 34K40
Mathematics Subject Classification ID: 34K45
zbMATH DE Number: 7439084
zbMATH Keywords: oscillation
zbMATH Keywords: non-oscillation
zbMATH Keywords: neutral
zbMATH Keywords: delay
zbMATH Keywords: Lebesgue's dominated convergence theorem
zbMATH Keywords: impulses
MaRDI profile type: Publication
full work available at URL: tmmp-2020-0025
OpenAlex ID: W3097811719
Wikidata QID: Q115227820
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DOI: 10.2478/TMMP-2020-0025
description: scientific article; zbMATH DE number 7439084