Oscillation criteria related to integral averaging technique for linear matrix Hamiltonian systems
type: Item
instance of: scholarly article
title: Oscillation criteria related to integral averaging technique for linear matrix Hamiltonian systems
zbMATH Open document ID: 1058.34038
published in: Journal of Mathematical Analysis and Applications
publication date: 2004-08-20T00:00:00Z
review text: New oscillation criteria are established for the linear matrix Hamiltonian system \[ U'=A(x)U+B(x)V,\quad V'=C(x)U-A^*(x)V, \tag{*} \] where \(A(x)\), \(B(x)=B^*(x)>0\) and \(C(x)=C^*(x)\) are \(n\times n\)-matrices of real-valued continuous functions on the interval \(I=[x_0,\infty)\). These results are obtained by using the generalized Riccati technique and the integral averaging technique introduced by \textit{Ch. G. Philos} (1989), and they generalize a number of existing results, e.g., results of \textit{L. H. Erbe, Q. Kong} and \textit{S. Ruan} [Proc. Am. Math. Soc. 117, No. 4, 957--962 (1993; Zbl 0777.34024)], \textit{I. Sowjanya Kumari} and \textit{S. Umamaheswaram} [J. Differ. Equations 165, No. 1, 174--198 (2000; Zbl 0970.34025)], \textit{H. J. Li} [J. Math. Anal. Appl. 194, 217--234 (1995; Zbl 0836.34033)] and \textit{Z. Zheng, F. Meng} and \textit{Y. Yu} [Acta Math. Sin. 41, No. 6, 1231--1238 (1998; Zbl 1018.34033)]. Three examples illustrate various oscillation criteria.
Mathematics Subject Classification ID: 34C10
Mathematics Subject Classification ID: 37J99
zbMATH DE Number: 2093791
zbMATH Keywords: matrix Hamiltonian system
zbMATH Keywords: oscillation
zbMATH Keywords: generalized Riccati technique
zbMATH Keywords: integral averaging technique
author: Qiru Wang
reviewed by: Zuzana Došlá
MaRDI profile type: Publication
full work available at URL: j.jmaa.2004.02.041
OpenAlex ID: W2007561268
cites work: Riccati Techniques and Variational Principles in Oscillation Theory for Linear Systems
cites work: Weighted means and oscillation conditions for second order matrix differential equations
cites work: Summability methods for oscillation of linear second-order matrix differential equations
cites work: Kamenev Type Theorems for Second Order Matrix Differential Systems
cites work: Oscillation criteria for second order self adjoint differential systems
cites work: On Non-Oscillatory Linear Differential Equations of Second Order
cites work: Oscillation criteria for self-adjoint second-order differential systems and ''Principal sectional curvatures''
cites work: Oscillation theory for generalized second-order differential equations
cites work: Q4167008
cites work: Oscillation criteria for linear matrix Hamiltonian systems
cites work: Oscillation criteria for second order linear differential equations
cites work: A note on Kamenev type theorems for second order matrix differential systems
cites work: On a Conjecture for Oscillation of Second Order Ordinary Differential Systems
cites work: Oscillation of linear second order matrix differential equations
cites work: Oscillation theorems for linear differential equations of second order
cites work: Sturmian theory for ordinary differential equations
cites work: Note on ``Oscillation criteria for second order linear differential equations''
cites work: Oscillation criteria for second-order matrix differential systems
cites work: A criterion of oscillatory stability
cites work: Q3154091
DOI: 10.1016/J.JMAA.2004.02.041
description: scientific article; zbMATH DE number 2093791