Oscillation and spectral theory for linear Hamiltonian systems with nonlinear dependence on the spectral parameter

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F12%3A00057204" target="_blank" >RIV/00216224:14310/12:00057204 - isvavai.cz</a>

Result on the web

<a href="http://dx.doi.org/10.1002/mana.201100172" target="_blank" >http://dx.doi.org/10.1002/mana.201100172</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1002/mana.201100172" target="_blank" >10.1002/mana.201100172</a>

Result language

angličtina

Original language name

Oscillation and spectral theory for linear Hamiltonian systems with nonlinear dependence on the spectral parameter

Original language description

In this paper, we consider linear Hamiltonian differential systems which depend in general nonlinearly on the spectral parameter and with Dirichlet boundary conditions. Our results generalize the known theory of linear Hamiltonian systems in two respects. Namely, we allow nonlinear dependence of the coefficients on the spectral parameter and at the same time we do not impose any controllability and strict normality assumptions. We introduce the notion of a finite eigenvalue and prove the oscillation theorem relating the number of finite eigenvalues which are less than or equal to a given value of the spectral parameter with the number of proper focal points of the principal solution of the system in the considered interval. We also define the corresponding geometric multiplicity of finite eigenvalues in terms of finite eigenfunctions and prove that the algebraic and geometric multiplicities coincide.

Czech name

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Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

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Project

<a href="/en/project/GC201%2F09%2FJ009" target="_blank" >GC201/09/J009: Oscillation and spectral theory of differential and difference systems</a><br>

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year

2012

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Mathematische Nachrichten

ISSN

0025-584X

e-ISSN

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Volume of the periodical

285

Issue of the periodical within the volume

11-12

Country of publishing house

DE - GERMANY

Number of pages

14

Pages from-to

1343-1356

UT code for WoS article

000307008700006

EID of the result in the Scopus database

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