Relative oscillation theory for linear Hamiltonian systems with nonlinear dependence on the spectral parameter

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Relative oscillation theory for linear Hamiltonian systems with nonlinear dependence on the spectral parameter

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Relative oscillation theory for linear Hamiltonian systems with nonlinear dependence on the spectral parameter

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA19-01246S" target="_blank" >GA19-01246S: Nová oscilační teorie pro lineární hamiltonovské a symplektické systémy</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2023

Kód důvěrnosti údajů

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

Název periodika

Mathematische Nachrichten

ISSN

0025-584X

e-ISSN

1522-2616

Svazek periodika

296

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

21

Strana od-do

196-216

Kód UT WoS článku

000876538800001

EID výsledku v databázi Scopus

2-s2.0-85125516106