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
ISBN
0096-3003
Periodical
APPLIED MATHEMATICS AND COMPUTATION
Year of study
243
Number
7
State
US
Pages from
838
Pages to
848
Pages count
11
URL
Documents
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"
}