Singular Sturmian comparison theorems for linear Hamiltonian systems

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F20%3A00114052" target="_blank" >RIV/00216224:14310/20:00114052 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.sciencedirect.com/science/article/pii/S0022039620300802?dgcid=author" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0022039620300802?dgcid=author</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jde.2020.02.016" target="_blank" >10.1016/j.jde.2020.02.016</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Singular Sturmian comparison theorems for linear Hamiltonian systems

Popis výsledku v původním jazyce

In this paper we prove singular comparison theorems on unbounded intervals for two nonoscillatory linear Hamiltonian systems satisfying the Sturmian majorant condition and the Legendre condition. At the same time we do not impose any controllability condition. The results are phrased in terms of the comparative index and the numbers of proper focal points of the (minimal) principal solutions of these systems at both endpoints of the considered interval. The main idea is based on an application of new transformation theorems for principal and antiprincipal solutions at infinity and on new limit properties of the comparative index involving these solutions. This work generalizes the recently obtained Sturmian separation theorems on unbounded intervals for one system by the authors (2019), as well as the Sturmian comparison theorems and transformation theorems on compact intervals by J. Elyseeva (2016 and 2018). We note that all the results are new even in the completely controllable case.

Název v anglickém jazyce

Singular Sturmian comparison theorems for linear Hamiltonian systems

Popis výsledku anglicky

In this paper we prove singular comparison theorems on unbounded intervals for two nonoscillatory linear Hamiltonian systems satisfying the Sturmian majorant condition and the Legendre condition. At the same time we do not impose any controllability condition. The results are phrased in terms of the comparative index and the numbers of proper focal points of the (minimal) principal solutions of these systems at both endpoints of the considered interval. The main idea is based on an application of new transformation theorems for principal and antiprincipal solutions at infinity and on new limit properties of the comparative index involving these solutions. This work generalizes the recently obtained Sturmian separation theorems on unbounded intervals for one system by the authors (2019), as well as the Sturmian comparison theorems and transformation theorems on compact intervals by J. Elyseeva (2016 and 2018). We note that all the results are new even in the completely controllable 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

2020

Kód důvěrnosti údajů

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

Název periodika

Journal of Differential Equations

ISSN

0022-0396

e-ISSN

—

Svazek periodika

269

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

36

Strana od-do

2920-2955

Kód UT WoS článku

000534488300007

EID výsledku v databázi Scopus

2-s2.0-85080043194