Special cases of critical linear difference equations

J 2021

Special cases of critical linear difference equations

JEKL, Jan

Základní údaje

Originální název

Special cases of critical linear difference equations

Autoři

JEKL, Jan

Vydání

Electronic Journal of Qualitative Theory of Differential Equations, Electronic Journal of Qualitative Theory of Differential Equations, 2021, 1417-3875

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10101 Pure mathematics

Stát vydavatele

Maďarsko

Utajení

není předmětem státního či obchodního tajemství

Odkazy

URL

Impakt faktor

Impact factor: 1.316

Označené pro přenos do RIV

Ano

Kód RIV

RIV/00216224:14310/21:00119263

Organizační jednotka

Přírodovědecká fakulta

Klíčová slova anglicky

critical equations; linear difference equations; equations with interlacing indices

Štítky

14311010, rivok

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 1. 11. 2021 13:34, Mgr. Marie Novosadová Šípková, DiS.

Anotace

V originále

In this paper, we investigate even-order linear difference equations and their criticality. However, we restrict our attention only to several special cases of the general Sturm–Liouville equation. We wish to investigate on such cases a possible converse of a known theorem. This theorem holds for second-order equations as an equivalence; however, only one implication is known for even-order equations. First, we show the converse in a sense for one term equations. Later, we show an upper bound on criticality for equations with nonnegative coefficients as well. Finally, we extend the criticality of the second-order linear self-adjoint equation for the class of equations with interlacing indices. In this way, we can obtain concrete examples aiding us with our investigation.

Návaznosti

GA20-11846S, projekt VaV

Název: Diferenciální a diferenční rovnice reálných řádů: kvalitativní analýza a její aplikace

Investor: Grantová agentura ČR, Diferenciální a diferenční rovnice reálných řádů: kvalitativní analýza a její aplikace

MUNI/A/1160/2020, interní kód MU

Název: Matematické struktury 10 (Akronym: Matematické struktury 10)

Investor: Masarykova univerzita, Matematické struktury 10

Citovat

JEKL, Jan. Special cases of critical linear difference equations. Electronic Journal of Qualitative Theory of Differential Equations. Electronic Journal of Qualitative Theory of Differential Equations, 2021, roč. 2021, č. 79, s. 1-17. ISSN 1417-3875. Dostupné z: https://doi.org/10.14232/ejqtde.2021.1.79.

@article{1797267,
   author = {Jekl, Jan},
   article_number = {79},
   doi = {https://doi.org/10.14232/ejqtde.2021.1.79},
   keywords = {critical equations; linear difference equations; equations with interlacing indices},
   language = {eng},
   issn = {1417-3875},
   journal = {Electronic Journal of Qualitative Theory of Differential Equations},
   title = {Special cases of critical linear difference equations},
   url = {https://doi.org/10.14232/ejqtde.2021.1.79},
   volume = {2021},
   year = {2021}
}

TY  - JOUR
ID  - 1797267
AU  - Jekl, Jan
PY  - 2021
TI  - Special cases of critical linear difference equations
JF  - Electronic Journal of Qualitative Theory of Differential Equations
VL  - 2021
IS  - 79
SP  - 1-17
EP  - 1-17
PB  - Electronic Journal of Qualitative Theory of Differential Equations
SN  - 14173875
KW  - critical equations
KW  - linear difference equations
KW  - equations with interlacing indices
UR  - https://doi.org/10.14232/ejqtde.2021.1.79
N2  - In this paper, we investigate even-order linear difference equations and their criticality. However, we restrict our attention only to several special cases of the general Sturm–Liouville equation. We wish to investigate on such cases a possible converse of a known theorem. This theorem holds for second-order equations as an equivalence; however, only one implication is known for even-order equations. First, we show the converse in a sense for one term equations. Later, we show an upper bound on criticality for equations with nonnegative coefficients as well. Finally, we extend the criticality of the second-order linear self-adjoint equation for the class of equations with interlacing indices. In this way, we can obtain concrete examples aiding us with our investigation.
ER  -

JEKL, Jan. Special cases of critical linear difference equations. \textit{Electronic Journal of Qualitative Theory of Differential Equations}. Electronic Journal of Qualitative Theory of Differential Equations, 2021, roč.~2021, č.~79, s.~1-17. ISSN~1417-3875. Dostupné z: https://doi.org/10.14232/ejqtde.2021.1.79.

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