Detail publikace

Oscillation constants for second-order nonlinear dynamic equations of Euler type on time scales

ŘEHÁK, P. YAMAOKA, N.

Anglický název

Oscillation constants for second-order nonlinear dynamic equations of Euler type on time scales

Typ

článek v časopise ve Web of Science, Jimp

Jazyk

en

Originální abstrakt

We are concerned with the oscillation problem for second-order nonlinear dynamic equations on time scales of the form $x^{\Delta \Delta} + f(x)/(t \sigma(t)) = 0$, where $f(x)$ satisfies $x f(x) > 0$ if $x \neq 0$. By means of Riccati technique and phase plane analysis of a system, (non)oscillation criteria are established. A necessary and sufficient condition for all nontrivial solutions of the Euler-Cauchy dynamic equation $y^{\Delta \Delta} +\lambda/(t \sigma(t))\, y = 0$ to be oscillatory plays a crucial role in proving our results.

Anglický abstrakt

We are concerned with the oscillation problem for second-order nonlinear dynamic equations on time scales of the form $x^{\Delta \Delta} + f(x)/(t \sigma(t)) = 0$, where $f(x)$ satisfies $x f(x) > 0$ if $x \neq 0$. By means of Riccati technique and phase plane analysis of a system, (non)oscillation criteria are established. A necessary and sufficient condition for all nontrivial solutions of the Euler-Cauchy dynamic equation $y^{\Delta \Delta} +\lambda/(t \sigma(t))\, y = 0$ to be oscillatory plays a crucial role in proving our results.

Klíčová slova anglicky

Oscillation constant; Dynamic equations on time scales; Euler-Cauchy equation; Riccati technique; Phase plane analysis; Schauder fixed point theorem

Vydáno

07.09.2017

Nakladatel

Taylor and Francis

ISSN

1563-5120

Ročník

23

Číslo

11

Strany od–do

1884–1900

Počet stran

17

BIBTEX


@article{BUT140805,
  author="Pavel {Řehák} and Naoto {Yamaoka},
  title="Oscillation constants for second-order nonlinear dynamic equations of Euler type on time scales",
  year="2017",
  volume="23",
  number="11",
  month="September",
  pages="1884--1900",
  publisher="Taylor and Francis",
  issn="1563-5120"
}