Dynamic Picone's identity and its applications
type: Item
instance of: scholarly article
title: Dynamic Picone's identity and its applications
zbMATH Open document ID: 1408.34074
author: Nguyen Du Vi Nhan
author: Dinh Thanh Duc
author: Tran Dinh Phung
author: Vu Kim Tuan
published in: Journal of Mathematical Analysis and Applications
publication date: 2018-10-18T00:00:00Z
review text: The authors establish Picone type identities and inequalities that are related to the nonlinear dynamic system \[ u^\Delta=Au^\sigma+B\varphi_{1/\alpha}(v), v^\Delta=-C\varphi_\alpha(u^\sigma)-Dv \] on a time scale, where \(\varphi_\alpha(t)=|t|^\alpha\text{sgn}t\), \(\alpha>0\), \(A,B,C,D\) are rd-continuous with \(B>0\), and \(-A\) and \(-D\) are positively regressive. Using these tools they derive Writinger and Hardy type inequalities on time scales which serve to study qualitative properties of the system. Among other, the Reid type roundabout theorem involving disconjugacy and Sturmian theorems are stated. Another aim of the paper is to correct the results from \textit{S. H. Saker} et al. [Appl. Math. Lett. 48, 162--169 (2015; Zbl 1323.26029)].
Mathematics Subject Classification ID: 34N05
Mathematics Subject Classification ID: 34C10
Mathematics Subject Classification ID: 26D15
zbMATH DE Number: 6957994
zbMATH Keywords: dynamic system
zbMATH Keywords: Picone's identity
zbMATH Keywords: Wirtinger's inequality
zbMATH Keywords: Hardy's inequality
zbMATH Keywords: Reid's roundabout theorem
zbMATH Keywords: Sturm's theory
reviewed by: Pavel Rehak
MaRDI profile type: Publication
full work available at URL: j.jmaa.2018.09.020
OpenAlex ID: W2891779737
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Wikidata QID: Q129240737
DOI: 10.1016/J.JMAA.2018.09.020
description: scientific article; zbMATH DE number 6957994