Detail publikace

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

Originální název

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

Anglický název

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

Jazyk

en

Originální abstrakt

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 $\gamma<\Gamma$.

Anglický abstrakt

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 $\gamma<\Gamma$.

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"
}