The nonoscillatory solutions of delay differential equations with impulses
type: Item
instance of: scholarly article
title: The nonoscillatory solutions of delay differential equations with impulses
zbMATH Open document ID: 0861.34044
DOI: 10.1016/S0096-3003(95)00198-0
published in: Applied Mathematics and Computation
publication date: 1997-05-13T00:00:00Z
review text: The author proves that eventually positive (negative) solutions of the scalar delay differential equation \(x'(t)=- \sum^n_{i=1} p_i(t) x(t-r_i(t))\), where \(p_i,r_i\in C([t_0,+\infty)), \mathbb{R}_+)\), \(\lim_{t\to+\infty} (t-r_i(t))= +\infty\), conserve their nonoscillatory properties under impulsive perturbations of the form \(x(t^+_k)- x(t_k)= I_k(x(t_k))\) with \(I_k(-u)= -I_k(u)\), \(uI_k(u)\geq 0\), \(\forall u\in \mathbb{R}\), \(k\in\mathbb{N}\), and \(t_k< t_{k+1}\to+\infty\) as \(k\to+\infty\).
Mathematics Subject Classification ID: 34K99
Mathematics Subject Classification ID: 34A37
zbMATH DE Number: 911908
zbMATH Keywords: impulsive differential equation with variable delays
zbMATH Keywords: nonoscillatory solution
zbMATH Keywords: initial value problem
zbMATH Keywords: comparison
author: Jianhua Shen
reviewed by: Sergei Trofimchuk
MaRDI profile type: Publication
cites work: Q3995625
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description: scientific article; zbMATH DE number 911908