Necessary and sufficient conditions for the oscillation of delay differential equations with a piecewise constant argument
type: Item
instance of: scholarly article
title: Necessary and sufficient conditions for the oscillation of delay differential equations with a piecewise constant argument
zbMATH Open document ID: 0904.34052
DOI: 10.1155/S0161171298000702
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1999-01-19T00:00:00Z
full work available at URL: https://eudml.org/doc/48042
review text: Summary: The characteristic equation for an equation with continuous and piecewise constant argument in the form \[ \dot x(t)+ px(t-\tau)+ qx([t- k])= 0,\quad\text{where }p, q\in\mathbb{R},\;\tau\in\mathbb{R}^+\text{ and }k\in \mathbb{N} \] is presented, which for \(q= 0\) reduces to \[ f(\lambda)= \lambda+ e^{-\lambda r}= 0 \] and for \(p= 0\) reduces to \[ \lambda- 1+ q\lambda^{-k}= 0. \] Necessary and sufficient conditions for oscillation are obtained.
Mathematics Subject Classification ID: 34K11
Mathematics Subject Classification ID: 39A10
zbMATH DE Number: 1180640
zbMATH Keywords: delay differential equations
zbMATH Keywords: oscillation
Wikidata QID: Q115243284
author: H. A. Agwo
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1180640