Solutions with prescribed numbers of focal points of nonoscillatory linear Hamiltonian systems

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F23%3A00134013" target="_blank" >RIV/00216224:14310/23:00134013 - isvavai.cz</a>

Výsledek na webu

<a href="https://link.springer.com/article/10.1007/s00605-022-01780-4" target="_blank" >https://link.springer.com/article/10.1007/s00605-022-01780-4</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00605-022-01780-4" target="_blank" >10.1007/s00605-022-01780-4</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Solutions with prescribed numbers of focal points of nonoscillatory linear Hamiltonian systems

Popis výsledku v původním jazyce

In this paper we present an existence result for conjoined bases of nonoscillatory linear Hamiltonian systems on an unbounded interval, which have prescribed numbers of left and right proper focal points. The result is based on a singular Sturmian separation theorem on an unbounded interval by the authors (2019) and it extends a similar property, which was recently derived for linear Hamiltonian systems on compact interval (2021). At the same time it is new even for completely controllable linear Hamiltonian systems, including higher order Sturm–Liouville differential equations. As the main tools we use the comparative index and properties of the minimal principal solution at infinity, which serves as the reference solution for calculating the numbers of proper focal points. We also provide several examples illustrating the presented theory.

Název v anglickém jazyce

Solutions with prescribed numbers of focal points of nonoscillatory linear Hamiltonian systems

Popis výsledku anglicky

In this paper we present an existence result for conjoined bases of nonoscillatory linear Hamiltonian systems on an unbounded interval, which have prescribed numbers of left and right proper focal points. The result is based on a singular Sturmian separation theorem on an unbounded interval by the authors (2019) and it extends a similar property, which was recently derived for linear Hamiltonian systems on compact interval (2021). At the same time it is new even for completely controllable linear Hamiltonian systems, including higher order Sturm–Liouville differential equations. As the main tools we use the comparative index and properties of the minimal principal solution at infinity, which serves as the reference solution for calculating the numbers of proper focal points. We also provide several examples illustrating the presented theory.

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

Monatshefte für Mathematik

ISSN

0026-9255

e-ISSN

1436-5081

Svazek periodika

200

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

AT - Rakouská republika

Počet stran výsledku

29

Strana od-do

359-387

Kód UT WoS článku

000876636600001

EID výsledku v databázi Scopus

2-s2.0-85140213986