Oscillation criteria for linear matrix Hamiltonian systems
type: Item
instance of: scholarly article
title: Oscillation criteria for linear matrix Hamiltonian systems
zbMATH Open document ID: 0970.34025
author: I. Sowjanya Kumari
author: S. Umamaheswaram
published in: Journal of Differential Equations
publication date: 2001-08-30T00:00:00Z
review text: The authors give some oscillation criteria for the linear matrix Hamiltonian system: \[ U'=A(x)U+B(x)V,\;V'=C(x)U-A^*(x)V,\tag{*} \] where \(A(x)\), \(B(x)=B^* (x)>0\) and \(C(x)=C^*(x)\) are real continuous \(n\times n\)-matrix functions on the interval \([a,\infty)\). The results given stand for extensions to the systems of the form (*), of the following oscillation criteria earlier derived by other authors: theorems 1 and 2 for the system (**) \(Y''+Q(x) Y=0\) due to \textit{G. J. Etgen} and \textit{J. F. Pawlowski} [Pacific J. Math. 66, 99-110 (1976; Zbl 0355.34017)] and theorems 1-7 of \textit{L. H. Erbe}, \textit{Q. Kong} and \textit{S. Ruan} [Proc. Am. Math. Soc. 117, No. 4, 957-962 (1993; Zbl 0777.34024)] for selfadjoint systems (***) \((P(x)U')'+ Q(x)U=0\) as well as the theorem 1 for (**) given by \textit{F. Meng}, \textit{J. Wang} and \textit{Z. Zheng} [Proc. Am. Math. Soc. 126, No. 2, 391-395 (1998; Zbl 0891.34037)]. Finally, the authors present a set of six examples illustrating the established theorems.
reviewed by: Nácere Hayek
Mathematics Subject Classification ID: 34C10
Mathematics Subject Classification ID: 34A30
zbMATH DE Number: 1538234
zbMATH Keywords: oscillation criteria
zbMATH Keywords: linear matrix differential systems
zbMATH Keywords: Kamenev-type theorems
MaRDI profile type: Publication
full work available at URL: jdeq.1999.3746
OpenAlex ID: W2037176458
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DOI: 10.1006/JDEQ.1999.3746
description: scientific article; zbMATH DE number 1538234