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VÍTOVEC, J.
Originální název
Critical oscillation constant for Euler-type dynamic equations on time scales
Typ
článek v časopise ve Web of Science, Jimp
Jazyk
angličtina
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 $\gamma<\Gamma$.
Klíčová slova
Time scale; Dynamic equation; Non(oscillation) criteria; Periodic coefficient
Autoři
Rok RIV
2014
Vydáno
9. 7. 2014
ISSN
0096-3003
Periodikum
APPLIED MATHEMATICS AND COMPUTATION
Ročník
243
Číslo
7
Stát
Spojené státy americké
Strany od
838
Strany do
848
Strany počet
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", journal="APPLIED MATHEMATICS AND COMPUTATION", year="2014", volume="243", number="7", pages="838--848", doi="10.1016/j.amc.2014.06.066", issn="0096-3003", url="http://www.sciencedirect.com/science/article/pii/S0096300314009096" }