Publication detail

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

ŘEHÁK, P. YAMAOKA, N.

English title

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

Type

WoS Article

Language

en

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.

Keywords in English

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

Released

2017-09-07

Publisher

Taylor and Francis

ISSN

1563-5120

Journal

JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS

Volume

23

Number

11

Pages from–to

1884–1900

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"
}