Detail publikačního výsledku

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

ŘEHÁK, P.; YAMAOKA, N.

Originální název

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

Anglický název

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

Druh

Článek WoS

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

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

Klíčová slova v angličtině

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

Autoři

ŘEHÁK, P.; YAMAOKA, N.

Rok RIV

2018

Vydáno

07.09.2017

Nakladatel

Taylor and Francis

ISSN

1563-5120

Periodikum

JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS

Svazek

23

Číslo

11

Stát

Spojené království Velké Británie a Severního Irska

Strany od

1884

Strany do

1900

Strany počet

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",
  journal="JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS",
  year="2017",
  volume="23",
  number="11",
  pages="1884--1900",
  doi="10.1080/10236198.2017.1371146",
  issn="1023-6198"
}