Relative oscillation theory for linear Hamiltonian systems with nonlinear dependence on the spectral parameter
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F23%3A00134063" target="_blank" >RIV/00216224:14310/23:00134063 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1002/mana.202000434" target="_blank" >https://doi.org/10.1002/mana.202000434</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1002/mana.202000434" target="_blank" >10.1002/mana.202000434</a>
Alternative languages
Result language
angličtina
Original language name
Relative oscillation theory for linear Hamiltonian systems with nonlinear dependence on the spectral parameter
Original language description
In this paper, we consider two linear Hamiltonian differential systems that depend in general nonlinearly on the spectral parameter lambda and with Dirichlet boundary conditions. For the Hamiltonian problems, we do not assume any controllability and strict normality assumptions and also omit the classical Legendre condition for their Hamiltonians. The main result of the paper, the relative oscillation theorem, relates the difference of the numbers of finite eigenvalues of the two problems in the intervals (-infinity,beta]$(-infty , beta ]$ and (-infinity,alpha]$(-infty , alpha ]$, respectively, with the so-called oscillation numbers associated with the Wronskian of the principal solutions of the systems evaluated for lambda=alpha$lambda =alpha$ and lambda=beta$lambda =beta$. As a corollary to the main result, we prove the renormalized oscillation theorems presenting the number of finite eigenvalues of one single problem in (alpha,beta]$(alpha ,beta ]$. The consideration is based on the comparative index theory applied to the continuous case.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA19-01246S" target="_blank" >GA19-01246S: New oscillation theory for linear Hamiltonian and symplectic systems</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Mathematische Nachrichten
ISSN
0025-584X
e-ISSN
1522-2616
Volume of the periodical
296
Issue of the periodical within the volume
1
Country of publishing house
DE - GERMANY
Number of pages
21
Pages from-to
196-216
UT code for WoS article
000876538800001
EID of the result in the Scopus database
2-s2.0-85125516106