Nonoscillation of first-order dynamic equations with several delays
type: Item
instance of: scholarly article
title: Nonoscillation of first-order dynamic equations with several delays
zbMATH Open document ID: 1216.34099
DOI: 10.1155/2010/873459
published in: Advances in Difference Equations
publication date: 2010-09-27T00:00:00Z
full work available at URL: https://eudml.org/doc/225352
review text: The authors study the delay dynamic equation with positive variable coefficients and multiple delays, of the form: \[ x^\Delta(t) + \sum_{i \in [1,n]_{\mathbb{T}}} A_i(t) x(\alpha_i(t)) = 0 , \quad\text{for }t \in [t_0, \infty)_{\mathbb{T}}, \] where \(\mathbb{T}\) is a time scale, and establish that nonoscillation is equivalent to the existence of a positive solution for the generalized characteristic inequality and to the positivity of the fundamental solution. A few comparison theorems between the solutions of two different equations and two different solutions of the same equation are proved. Several examples of non standard time scales are also provided to illustrate the nonoscillatory criterion for dynamic equations that are different from delay differential and classical difference equations. It is also shown that, if the above dynamic equation is nonoscillatory, then it has no slowly oscillating solutions. A few important open problems are suggested.
Mathematics Subject Classification ID: 34N05
Mathematics Subject Classification ID: 34K11
zbMATH DE Number: 5791591
zbMATH Keywords: nonoscillation
zbMATH Keywords: dynamic equations with delays
zbMATH Keywords: positive solution
zbMATH Keywords: comparison theorems
Wikidata QID: Q59253469
author: E. Braverman
author: Basak Karpuz
reviewed by: Gnana Bhaskar Tenali
MaRDI profile type: Publication
OpenAlex ID: W1970293791
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description: scientific article; zbMATH DE number 5791591