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

J 2023

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

ŠEPITKA, Peter a Roman ŠIMON HILSCHER

Základní údaje

Originální název

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

Autoři

ŠEPITKA, Peter a Roman ŠIMON HILSCHER

Vydání

Monatshefte für Mathematik, Springer, 2023, 0026-9255

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10101 Pure mathematics

Stát vydavatele

Rakousko

Utajení

není předmětem státního či obchodního tajemství

Odkazy

URL

Impakt faktor

Impact factor: 0.800

Označené pro přenos do RIV

Ano

Kód RIV

RIV/00216224:14310/23:00134013

Organizační jednotka

Přírodovědecká fakulta

Klíčová slova anglicky

Linear Hamiltonian system; Left proper focal point; Right proper focal point; Comparative index; Principal solution Singular; Sturmian separation theorem; Nonoscillation

Štítky

14311010, rivok

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 6. 2. 2023 11:04, Mgr. Marie Novosadová Šípková, DiS.

Anotace

V originále

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.

Návaznosti

GA19-01246S, projekt VaV

Název: Nová oscilační teorie pro lineární hamiltonovské a symplektické systémy

Investor: Grantová agentura ČR, Nová oscilační teorie pro lineární hamiltonovské a symplektické systémy

Citovat

ŠEPITKA, Peter a Roman ŠIMON HILSCHER. Solutions with prescribed numbers of focal points of nonoscillatory linear Hamiltonian systems. Monatshefte für Mathematik. Springer, 2023, roč. 200, č. 2, s. 359-387. ISSN 0026-9255. Dostupné z: https://doi.org/10.1007/s00605-022-01780-4.

@article{2225399,
   author = {Šepitka, Peter and Šimon Hilscher, Roman},
   article_number = {2},
   doi = {https://doi.org/10.1007/s00605-022-01780-4},
   keywords = {Linear Hamiltonian system; Left proper focal point; Right proper focal point; Comparative index; Principal solution Singular; Sturmian separation theorem; Nonoscillation},
   language = {eng},
   issn = {0026-9255},
   journal = {Monatshefte für Mathematik},
   title = {Solutions with prescribed numbers of focal points of nonoscillatory linear Hamiltonian systems},
   url = {https://link.springer.com/article/10.1007/s00605-022-01780-4},
   volume = {200},
   year = {2023}
}

TY  - JOUR
ID  - 2225399
AU  - Šepitka, Peter - Šimon Hilscher, Roman
PY  - 2023
TI  - Solutions with prescribed numbers of focal points of nonoscillatory linear Hamiltonian systems
JF  - Monatshefte für Mathematik
VL  - 200
IS  - 2
SP  - 359-387
EP  - 359-387
PB  - Springer
SN  - 00269255
KW  - Linear Hamiltonian system
KW  - Left proper focal point
KW  - Right proper focal point
KW  - Comparative index
KW  - Principal solution Singular
KW  - Sturmian separation theorem
KW  - Nonoscillation
UR  - https://link.springer.com/article/10.1007/s00605-022-01780-4
N2  - 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.
ER  -

ŠEPITKA, Peter a Roman ŠIMON HILSCHER. Solutions with prescribed numbers of focal points of nonoscillatory linear Hamiltonian systems. \textit{Monatshefte für Mathematik}. Springer, 2023, roč.~200, č.~2, s.~359-387. ISSN~0026-9255. Dostupné z: https://doi.org/10.1007/s00605-022-01780-4.

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