Boundedness of solutions for singular Hamiltonian differential systems with applications to deficiency indices
type: Item
instance of: scholarly article
title: Boundedness of solutions for singular Hamiltonian differential systems with applications to deficiency indices
zbMATH Open document ID: 1116.34031
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2007-01-11T00:00:00Z
review text: Using special properties of Hamiltonian differential systems, the author obtains boundedness estimates of solutions for the higher-dimensional Hamiltonian differential system \[ Jy'(t)=[\lambda W(t)+P(t)]y(t) \] over the interval \(R^+=[0,+\infty)\), where \(\lambda\) is a complex parameter, \(J=\left( \begin{matrix} 0, & -I\\ I, & 0 \end{matrix} \right)\), \(I\) is the \(n\times n\) identity matrix and \(P^\ast(t)=P(t)\), \(W^\ast(t)=W(t)\geq 0\) are locally integrable \(2n\times 2n\) complex-valued Hermitean matrices (\(W(t)\) is nonnegative definite). As corollaries limit-circle criteria are established, one special case of which improves the results in [\textit{B. J. Harris}, ``Limit-circle criteria for second order differential expressions'', Q. J. Math., Oxf. II. Ser. 35, 415--427 (1984; Zbl 0558.34030)].
Mathematics Subject Classification ID: 34C11
Mathematics Subject Classification ID: 34B20
Mathematics Subject Classification ID: 37J99
Mathematics Subject Classification ID: 34D05
zbMATH DE Number: 5115289
zbMATH Keywords: singular Hamiltonian systems
zbMATH Keywords: asymptotic behavior
zbMATH Keywords: boundedness
zbMATH Keywords: limit-circle case
author: Jiangang Qi
reviewed by: Boris V. Loginov
MaRDI profile type: Publication
full work available at URL: j.na.2005.12.008
OpenAlex ID: W2077957297
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DOI: 10.1016/J.NA.2005.12.008
description: scientific article; zbMATH DE number 5115289