Publication detail

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

HASIL, P. VÍTOVEC, J.

Original Title

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

Type

journal article in Web of Science

Language

English

Original Abstract

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.

Keywords

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

Authors

HASIL, P.; VÍTOVEC, J.

RIV year

2015

Released

18. 2. 2015

Publisher

University of Szeged

ISBN

1417-3875

Periodical

Electronic Journal of Qualitative Theory of Differential Equations

Year of study

2015

Number

6

State

Hungary

Pages from

1

Pages to

24

Pages count

24

URL

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

Full text in the Digital Library

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"
}