Note on singular Sturm comparison theorem and strict majorant condition

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F24%3A00139407" target="_blank" >RIV/00216224:14310/24:00139407 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.sciencedirect.com/science/article/pii/S0022247X24003135" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0022247X24003135</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jmaa.2024.128391" target="_blank" >10.1016/j.jmaa.2024.128391</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Note on singular Sturm comparison theorem and strict majorant condition

Popis výsledku v původním jazyce

In this note we present a singular Sturm comparison theorem for two linear Hamiltonian systems satisfying a standard majorant condition and the identical normality assumption. Both endpoints of the considered interval may be singular. We identify the exact form of the strict majorant condition, which is necessary and sufficient for the property that every solution (conjoined basis) of the majorant system has more focal points than the solutions of the minorant system. We provide a formula for the exact number of focal points of any solution of the majorant system, depending on the number of focal points of solutions of the minorant system and on the number of right focal points of a solution of a certain transformed linear Hamiltonian system. This transformed system may be in general abnormal. Our result extends the previous Sturm comparison theorems for linear Hamiltonian systems by Kratz (1995) [18] on a compact interval and by the authors (2020) [35], [36] on an open or unbounded interval. The main result is also new for the second order differential equations, where it extends the singular comparison theorem by Aharonov and Elias (2010) [1].

Název v anglickém jazyce

Note on singular Sturm comparison theorem and strict majorant condition

Popis výsledku anglicky

In this note we present a singular Sturm comparison theorem for two linear Hamiltonian systems satisfying a standard majorant condition and the identical normality assumption. Both endpoints of the considered interval may be singular. We identify the exact form of the strict majorant condition, which is necessary and sufficient for the property that every solution (conjoined basis) of the majorant system has more focal points than the solutions of the minorant system. We provide a formula for the exact number of focal points of any solution of the majorant system, depending on the number of focal points of solutions of the minorant system and on the number of right focal points of a solution of a certain transformed linear Hamiltonian system. This transformed system may be in general abnormal. Our result extends the previous Sturm comparison theorems for linear Hamiltonian systems by Kratz (1995) [18] on a compact interval and by the authors (2020) [35], [36] on an open or unbounded interval. The main result is also new for the second order differential equations, where it extends the singular comparison theorem by Aharonov and Elias (2010) [1].

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA23-05242S" target="_blank" >GA23-05242S: Oscilační teorie na hybridních časových doménách s aplikacemi ve spektrální teorii a maticové analýze</a><br>

Návaznosti

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

Rok uplatnění

2024

Kód důvěrnosti údajů

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

Název periodika

Journal of Mathematical Analysis and Applications

ISSN

0022-247X

e-ISSN

1096-0813

Svazek periodika

538

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

16

Strana od-do

1-16

Kód UT WoS článku

001229936600001

EID výsledku v databázi Scopus

2-s2.0-85190308968