Nonoscillation of half-linear dynamic equations on time scales

J 2021

Nonoscillation of half-linear dynamic equations on time scales

HASIL, Petr, Jozef KISEL'ÁK, Michal POSPÍŠIL a Michal VESELÝ

Základní údaje

Originální název

Nonoscillation of half-linear dynamic equations on time scales

Autoři

HASIL, Petr (203 Česká republika, domácí), Jozef KISEL'ÁK, Michal POSPÍŠIL a Michal VESELÝ (203 Česká republika, garant, domácí)

Vydání

Mathematical Methods in the Applied Sciences, Wiley, 2021, 0170-4214

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10101 Pure mathematics

Stát vydavatele

Spojené státy

Utajení

není předmětem státního či obchodního tajemství

Odkazy

URL

Impakt faktor

Impact factor: 3.007

Kód RIV

RIV/00216224:14310/21:00119173

Organizační jednotka

Přírodovědecká fakulta

DOI

http://dx.doi.org/10.1002/mma.7304

UT WoS

000627606600001

Klíčová slova anglicky

dynamic equation; half‐ linear equation; linear equation; oscillation; Riccati equation; time scale

Štítky

rivok

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 1. 9. 2021 09:05, Mgr. Marie Šípková, DiS.

Anotace

V originále

The research contained in this paper belongs to the qualitative theory of dynamic equations on time scales. Via the detailed analysis of solutions of the associated Riccati equation and an advanced averaging technique, we provide the description of domain of nonoscillation of very general equations. The results are formulated and proved for half-linear equations (i.e., equations connected to PDEs with one dimensional p-Laplacian) on time scales. Nevertheless, we obtain new results also for linear difference equations. Moreover, the combination of the presented results with previous ones shows that many useful equations are conditionally oscillatory. Such equations are ideal as testing and comparison equations in real-world models which are beyond capabilities of known oscillation and nonoscillation criteria often.

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

Citovat

HASIL, Petr, Jozef KISEL'ÁK, Michal POSPÍŠIL a Michal VESELÝ. Nonoscillation of half-linear dynamic equations on time scales. Mathematical Methods in the Applied Sciences. Wiley, 2021, roč. 44, č. 11, s. 8775-8797. ISSN 0170-4214. Dostupné z: https://dx.doi.org/10.1002/mma.7304.

@article{1789197,
   author = {Hasil, Petr and Kisel'ák, Jozef and Pospíšil, Michal and Veselý, Michal},
   article_number = {11},
   doi = {http://dx.doi.org/10.1002/mma.7304},
   keywords = {dynamic equation; half‐ linear equation; linear equation; oscillation; Riccati equation; time scale},
   language = {eng},
   issn = {0170-4214},
   journal = {Mathematical Methods in the Applied Sciences},
   title = {Nonoscillation of half-linear dynamic equations on time scales},
   url = {https://doi.org/10.1002/mma.7304},
   volume = {44},
   year = {2021}
}

TY  - JOUR
ID  - 1789197
AU  - Hasil, Petr - Kisel'ák, Jozef - Pospíšil, Michal - Veselý, Michal
PY  - 2021
TI  - Nonoscillation of half-linear dynamic equations on time scales
JF  - Mathematical Methods in the Applied Sciences
VL  - 44
IS  - 11
SP  - 8775-8797
EP  - 8775-8797
PB  - Wiley
SN  - 01704214
KW  - dynamic equation
KW  - half‐ linear equation
KW  - linear equation
KW  - oscillation
KW  - Riccati equation
KW  - time scale
UR  - https://doi.org/10.1002/mma.7304
N2  - The research contained in this paper belongs to the qualitative theory of dynamic equations on time scales. Via the detailed analysis of solutions of the associated Riccati equation and an advanced averaging technique, we provide the description of domain of nonoscillation of very general equations. The results are formulated and proved for half-linear equations (i.e., equations connected to PDEs with one dimensional p-Laplacian) on time scales. Nevertheless, we obtain new results also for linear difference equations. Moreover, the combination of the presented results with previous ones shows that many useful equations are conditionally oscillatory. Such equations are ideal as testing and comparison equations in real-world models which are beyond capabilities of known oscillation and nonoscillation criteria often.
ER  -

HASIL, Petr, Jozef KISEL'ÁK, Michal POSPÍŠIL a Michal VESELÝ. Nonoscillation of half-linear dynamic equations on time scales. \textit{Mathematical Methods in the Applied Sciences}. Wiley, 2021, roč.~44, č.~11, s.~8775-8797. ISSN~0170-4214. Dostupné z: https://dx.doi.org/10.1002/mma.7304.

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