Detail publikačního výsledku

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

HASIL, P.; VÍTOVEC, J.

Originální název

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

Anglický název

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

Druh

Článek WoS

Originální abstrakt

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.

Anglický abstrakt

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.

Klíčová slova

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

Klíčová slova v angličtině

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

Autoři

HASIL, P.; VÍTOVEC, J.

Rok RIV

2016

Vydáno

18.02.2015

Nakladatel

University of Szeged

ISSN

1417-3875

Periodikum

Electronic Journal of Qualitative Theory of Differential Equations

Svazek

2015

Číslo

6

Stát

Maďarsko

Strany od

1

Strany do

24

Strany počet

24

URL

http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=3610

Plný text v Digitální knihovně

http://hdl.handle.net/11012/201405

BibTex

@article{BUT112975,
  author="Petr {Hasil} and Jiří {Vítovec}",
  title="Conditional oscillation of half-linear Euler-type dynamic equations on time scales",
  journal="Electronic Journal of Qualitative Theory of Differential Equations",
  year="2015",
  volume="2015",
  number="6",
  pages="1--24",
  doi="10.14232/ejqtde.2015.1.6",
  issn="1417-3875",
  url="http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=3610"
}