Nonoscillation of second-order dynamic equations with several delays
type: Item
instance of: scholarly article
title: Nonoscillation of second-order dynamic equations with several delays
zbMATH Open document ID: 1217.34139
DOI: 10.1155/2011/591254
author: Basak Karpuz
author: E. Braverman
published in: Abstract and Applied Analysis
publication date: 2011-05-16T00:00:00Z
full work available at URL: https://eudml.org/doc/227706
review text: Summary: The existence of nonoscillatory solutions for the second-order dynamic equation \[ (A_0,x^\Delta)^\Delta(t)+\sum_{i\in[1,n]_{\mathbb N}}A_i(t)x(\alpha_i(t))=0\text{ for }t\in [t_0,\infty)_{\mathbb T} \] is investigated in this paper. The results involve nonoscillation criteria in terms of relevant dynamic and generalized characteristic inequalities, comparison theorems, and explicit nonoscillation and oscillation conditions. This allows us to obtain most known nonoscillation results for second-order delay differential equations in the case \(A_0(t)\equiv 1\) for \(t\in [t_0,\infty)_{\mathbb R}\) and for second-order nondelay difference equations \((\alpha_i(t)=t+1\) for \(t\in [0,\infty)_{\mathbb N})\). Moreover, the general results imply new nonoscillation tests for delay differential equations with arbitrary \(A_0\) and for second-order delay difference equations. Known nonoscillation results for quantum scales can also be deduced.
Mathematics Subject Classification ID: 34N05
Mathematics Subject Classification ID: 34K11
zbMATH DE Number: 5888143
Wikidata QID: Q58654330
MaRDI profile type: Publication
OpenAlex ID: W2153995885
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description: scientific article; zbMATH DE number 5888143