Publication detail

Critical oscillation constant for Euler-type dynamic equations on time scales

VÍTOVEC, J.

Original Title

Critical oscillation constant for Euler-type dynamic equations on time scales

English Title

Critical oscillation constant for Euler-type dynamic equations on time scales

Type

journal article in Web of Science

Language

en

Original Abstract

In this paper we study the second-order dynamic equation on the time scale $\T$ of the form $$(r(t)y^{\Delta })^\Delta + \frac{\gamma q(t)}{t\sigma(t)}y^{\sigma}=0,$$ where $r$, $q$ are positive rd-continuous periodic functions with $\inf\{r(t),\, t\in\T\}>0$ and $\gamma$ is an arbitrary real constant. This equation corresponds to Euler-type differential (resp. Euler-type difference) equation for continuous (resp. discrete) case. Our aim is to prove that this equation is conditionally oscillatory, i.e., there exists a constant $\Gamma>0$ such that studied equation is oscillatory for $\gamma>\Gamma$ and non-oscillatory for $\gamma<\Gamma$.

English abstract

In this paper we study the second-order dynamic equation on the time scale $\T$ of the form $$(r(t)y^{\Delta })^\Delta + \frac{\gamma q(t)}{t\sigma(t)}y^{\sigma}=0,$$ where $r$, $q$ are positive rd-continuous periodic functions with $\inf\{r(t),\, t\in\T\}>0$ and $\gamma$ is an arbitrary real constant. This equation corresponds to Euler-type differential (resp. Euler-type difference) equation for continuous (resp. discrete) case. Our aim is to prove that this equation is conditionally oscillatory, i.e., there exists a constant $\Gamma>0$ such that studied equation is oscillatory for $\gamma>\Gamma$ and non-oscillatory for $\gamma<\Gamma$.

Keywords

Time scale; Dynamic equation; Non(oscillation) criteria; Periodic coefficient

RIV year

2014

Released

09.07.2014

Pages from

838

Pages to

848

Pages count

11

URL

http://www.sciencedirect.com/science/article/pii/S0096300314009096

BibTex 


@article{BUT108316,
  author="Jiří {Vítovec}",
  title="Critical oscillation constant for Euler-type dynamic equations on time scales",
  annote="In this paper we study the second-order dynamic equation on the time scale $\T$ of the form $$(r(t)y^{\Delta })^\Delta + \frac{\gamma q(t)}{t\sigma(t)}y^{\sigma}=0,$$  where $r$, $q$ are positive rd-continuous periodic functions with $\inf\{r(t),\, t\in\T\}>0$ and $\gamma$ is an arbitrary real constant. This equation corresponds to Euler-type differential (resp. Euler-type difference) equation for continuous (resp. discrete) case. Our aim is to prove that this equation is conditionally oscillatory, i.e., there exists a constant $\Gamma>0$ such that studied equation is oscillatory for $\gamma>\Gamma$ and non-oscillatory for $\gamma<\Gamma$.",
  chapter="108316",
  doi="10.1016/j.amc.2014.06.066",
  howpublished="online",
  number="7",
  volume="243",
  year="2014",
  month="july",
  pages="838--848",
  type="journal article in Web of Science"
}