Conditional oscillation of half-linear Euler-type dynamic
equations on time scales

J 2015

Conditional oscillation of half-linear Euler-type dynamic equations on time scales

HASIL, Petr and Jiří VÍTOVEC

Basic information

Original name

Conditional oscillation of half-linear Euler-type dynamic equations on time scales

Name in Czech

Podmíněná oscilace pololineární dynamické rovnice Eulerova typu na časových škálách

Authors

HASIL, Petr and Jiří VÍTOVEC

Edition

Electronic Journal of Qualitative Theory of Differential Equations, Szeged, University of Szeged, 2015, 1417-3875

Other information

Language

English

Type of outcome

Article in a journal

Field of Study

10101 Pure mathematics

Country of publisher

Hungary

Confidentiality degree

is not subject to a state or trade secret

References:

Full Text

Impact factor

Impact factor: 0.732

Organization unit

Faculty of Science

DOI

https://doi.org/10.14232/ejqtde.2015.1.6

UT WoS

000350397800001

EID Scopus

2-s2.0-84923171786

Keywords (in Czech)

Riccatiho technika; oscilační teorie; dynamická rovnice; časová škála; oscilační konstanta; podmíněná oscilace; pololineární rovnice; Eulerova rovnice

Keywords in English

time scale; conditional oscillation; Riccati technique; half-linear equation; dynamic equation; oscillation theory; Euler equation; oscillation constant

Abstract

ORIG CZ

In the original language

We investigate second-order half-linear Euler-type dynamic equations on time scales with positive periodic coefficients. We show that these equations are conditionally oscillatory, i.e., there exists a sharp borderline (a constant given by the coefficients of the given equation) between oscillation and non-oscillation of these equations. In addition, we explicitly find this so-called critical constant. In the cases that the time scale is reals or integers, our result corresponds to the classical results as well as in the case that the coefficients are replaced by constants and we take into account the linear equations. An example and corollaries are provided as well.

In Czech

Zkoumáme pololineární Eulerovy dynamické rovnice druhého řádu na časových škálách s kladnými periodickými koeficienty. Ukážeme, že tyto rovnice jsou podmíněně oscilatorické, tj. existuje přesná hranice (konstanta zadaná pomocí koeficientů dané rovnice) mezi oscilací a neoscilací těchto rovnic. Navíc tuto takzvanou kritickou konstantu explicitně určíme. V případě, že časová škála jsou reálná čísla nebo celá čísla, naše výsledky odpovídají klasickým výsledkům stejně jako případ, že koeficienty zkoumané rovnice jsou nahrazeny konstantami a uvažujeme lineární rovnici. Příklad a další důsledky jsou též uvedeny.

Cite

HASIL, Petr and Jiří VÍTOVEC. Conditional oscillation of half-linear Euler-type dynamic equations on time scales. Electronic Journal of Qualitative Theory of Differential Equations. Szeged: University of Szeged, 2015, vol. 2015, No 6, p. 1-24. ISSN 1417-3875. Available from: https://doi.org/10.14232/ejqtde.2015.1.6.

@article{1227192,
   author = {Hasil, Petr and Vítovec, Jiří},
   article_location = {Szeged},
   article_number = {6},
   doi = {https://doi.org/10.14232/ejqtde.2015.1.6},
   keywords = {time scale; conditional oscillation; Riccati technique; half-linear equation; dynamic equation; oscillation theory; Euler equation; oscillation constant},
   language = {eng},
   issn = {1417-3875},
   journal = {Electronic Journal of Qualitative Theory of Differential Equations},
   note = {Žádný z autorů nemá afiliaci na MU.},
   title = {Conditional oscillation of half-linear Euler-type dynamic equations on time scales},
   url = {http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=3610},
   volume = {2015},
   year = {2015}
}

TY  - JOUR
ID  - 1227192
AU  - Hasil, Petr - Vítovec, Jiří
PY  - 2015
TI  - Conditional oscillation of half-linear Euler-type dynamic equations on time scales
JF  - Electronic Journal of Qualitative Theory of Differential Equations
VL  - 2015
IS  - 6
SP  - 1-24
EP  - 1-24
PB  - University of Szeged
SN  - 14173875
N1  - Žádný z autorů nemá afiliaci na MU.
KW  - time scale
KW  - conditional oscillation
KW  - Riccati technique
KW  - half-linear equation
KW  - dynamic equation
KW  - oscillation theory
KW  - Euler equation
KW  - oscillation constant
UR  - http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=3610
N2  - We investigate second-order half-linear Euler-type dynamic equations on time scales with positive periodic coefficients. We show that these equations are conditionally oscillatory, i.e., there exists a sharp borderline (a constant given by the coefficients of the given equation) between oscillation and non-oscillation of these equations. In addition, we explicitly find this so-called critical constant. In the cases that the time scale is reals or integers, our result corresponds to the classical results as well as in the case that the coefficients are replaced by constants and we take into account the linear equations. An example and corollaries are provided as well.
ER  -

HASIL, Petr and Jiří VÍTOVEC. Conditional oscillation of half-linear Euler-type dynamic equations on time scales. \textit{Electronic Journal of Qualitative Theory of Differential Equations}. Szeged: University of Szeged, 2015, vol.~2015, No~6, p.~1-24. ISSN~1417-3875. Available from: https://doi.org/10.14232/ejqtde.2015.1.6.

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