Oscillation and spectral theory for linear Hamiltonian systems with nonlinear dependence on the spectral parameter
type: Item
instance of: scholarly article
title: Oscillation and spectral theory for linear Hamiltonian systems with nonlinear dependence on the spectral parameter
zbMATH Open document ID: 1254.34119
author: Werner Kratz
author: Martin Bohner
author: Roman Šimon Hilscher
published in: Mathematische Nachrichten
publication date: 2012-09-06T00:00:00Z
Mathematics Subject Classification ID: 34L05
Mathematics Subject Classification ID: 34C10
Mathematics Subject Classification ID: 34A30
Mathematics Subject Classification ID: 34B09
zbMATH DE Number: 6078245
zbMATH Keywords: linear Hamiltonian system
zbMATH Keywords: self-adjoint eigenvalue problem
zbMATH Keywords: proper focal point
zbMATH Keywords: conjoined basis
zbMATH Keywords: finite eigenvalue
zbMATH Keywords: oscillation theorem
zbMATH Keywords: normality
zbMATH Keywords: quadratic functional
MaRDI profile type: Publication
full work available at URL: mana.201100172
OpenAlex ID: W2166789854
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cites work: On the Eigenvalue Accumulation of Sturm-Liouville Problems Depending Nonlinearly on the Spectral Parameter
cites work: Q5613350
cites work: Riccati differential equations
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DOI: 10.1002/MANA.201100172
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review text: The authors consider linear Hamiltonian differential systems with Dirichlet boundary conditions, which depend in general nonlinearly on the spectral parameter. Without the controllability (or normality) assumption, they determine the finite eigenvalues and prove an oscillation theorem. They also determine the corresponding geometric multiplicity of the finite eigenvalues and prove that the algebraic and geometric multiplicities coincide.
reviewed by: Yulian An
description: scientific article; zbMATH DE number 6078245