Publication result detail

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

ŘEHÁK, P.; YAMAOKA, N.

Original Title

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

English Title

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

Type

WoS Article

Original Abstract

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.

English abstract

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.

Keywords

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

Key words in English

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

Authors

ŘEHÁK, P.; YAMAOKA, N.

RIV year

2018

Released

07.09.2017

Publisher

Taylor and Francis

ISBN

1563-5120

Periodical

JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS

Volume

23

Number

11

State

United Kingdom of Great Britain and Northern Ireland

Pages from

1884

Pages to

1900

Pages count

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"
}