Publication detail

A telescoping principle for oscillation of the second order half-linear dynamic equations on time scales

VÍTOVEC, J.

Original Title

A telescoping principle for oscillation of the second order half-linear dynamic equations on time scales

English Title

A telescoping principle for oscillation of the second order half-linear dynamic equations on time scales

Type

journal article - other

Language

en

Original Abstract

We establish the so-called ``telescoping principle" for oscillation of the second order half-linear dynamic equation $$\Bl[r(t)\Phi\bl(x^{\Delta }\br)\Br]^\Delta + c(t)\Phi(x^\sigma)=0$$ on a time scale. This principle provides a method enabling us to construct many new oscillatory equations. Unlike previous works concerning the telescoping principle, we formulate some oscillation results under the weaker assumption $r(t)\not=0$ (instead $r(t)>0$).

English abstract

We establish the so-called ``telescoping principle" for oscillation of the second order half-linear dynamic equation $$\Bl[r(t)\Phi\bl(x^{\Delta }\br)\Br]^\Delta + c(t)\Phi(x^\sigma)=0$$ on a time scale. This principle provides a method enabling us to construct many new oscillatory equations. Unlike previous works concerning the telescoping principle, we formulate some oscillation results under the weaker assumption $r(t)\not=0$ (instead $r(t)>0$).

Keywords

Half-linear dynamic equation; Telescoping principle; Oscillation criteria

RIV year

2009

Released

01.11.2009

Pages from

243

Pages to

255

Pages count

13

BibTex


@article{BUT50470,
  author="Jiří {Vítovec}",
  title="A telescoping principle for oscillation of the second order half-linear dynamic equations on time scales",
  annote="We establish the so-called ``telescoping principle" for oscillation of the second order half-linear dynamic equation $$\Bl[r(t)\Phi\bl(x^{\Delta }\br)\Br]^\Delta + c(t)\Phi(x^\sigma)=0$$ on a time scale. This principle provides a method enabling us to construct many new oscillatory equations. Unlike previous works concerning the telescoping principle, we formulate some oscillation results under the weaker assumption $r(t)\not=0$ (instead $r(t)>0$).",
  chapter="50470",
  journal="Tatra Mountains Mathematical Publications",
  number="11",
  volume="43",
  year="2009",
  month="november",
  pages="243--255",
  type="journal article - other"
}