Publication detail

# On asymptotic relationships between two higher order dynamic equations on time scales

ŘEHÁK, P.

Original Title

On asymptotic relationships between two higher order dynamic equations on time scales

English Title

On asymptotic relationships between two higher order dynamic equations on time scales

Type

journal article in Web of Science

Language

en

Original Abstract

We consider the $n$-th order dynamic equations $x^{\Delta^n}\!+p_1(t)x^{\Delta^{n-1}}+\cdots+p_n(t)x=0$ and $y^{\Delta^n}+p_1(t)y^{\Delta^{n-1}}+\cdots+p_n(t)y=f(t,y(\tau(t)))$ on a time scale $\mathbb{T}$, where $\tau$ is a composition of the forward jump operators, $p_i$ are real rd-continuous functions and $f$ is a continuous function; $\mathbb{T}$ is assumed to be unbounded above. We establish conditions that guarantee asymptotic equivalence between some solutions of these equations. No restriction is placed on whether the solutions are oscillatory or nonoscillatory. Applications to second order Emden-Fowler type dynamic equations and Euler type dynamic equations are shown.

English abstract

We consider the $n$-th order dynamic equations $x^{\Delta^n}\!+p_1(t)x^{\Delta^{n-1}}+\cdots+p_n(t)x=0$ and $y^{\Delta^n}+p_1(t)y^{\Delta^{n-1}}+\cdots+p_n(t)y=f(t,y(\tau(t)))$ on a time scale $\mathbb{T}$, where $\tau$ is a composition of the forward jump operators, $p_i$ are real rd-continuous functions and $f$ is a continuous function; $\mathbb{T}$ is assumed to be unbounded above. We establish conditions that guarantee asymptotic equivalence between some solutions of these equations. No restriction is placed on whether the solutions are oscillatory or nonoscillatory. Applications to second order Emden-Fowler type dynamic equations and Euler type dynamic equations are shown.

Keywords

higher order dynamic equation; time scale; asymptotic equivalence

Released

23.04.2017

Publisher

Elsevier

Pages from

84

Pages to

90

Pages count

7

URL

BibTex

```
@article{BUT135851,
author="Pavel {Řehák}",
title="On asymptotic relationships between two higher order dynamic equations on time scales",
annote="We consider the $n$-th order dynamic equations $x^{\Delta^n}\!+p_1(t)x^{\Delta^{n-1}}+\cdots+p_n(t)x=0$ and $y^{\Delta^n}+p_1(t)y^{\Delta^{n-1}}+\cdots+p_n(t)y=f(t,y(\tau(t)))$ on a time scale $\mathbb{T}$, where $\tau$ is a composition of the forward jump operators, $p_i$ are real rd-continuous functions and $f$ is a continuous function; $\mathbb{T}$ is assumed to be unbounded above. We establish conditions that guarantee asymptotic equivalence between some solutions of these equations. No restriction is placed on whether the solutions are oscillatory or nonoscillatory. Applications to second order Emden-Fowler type dynamic equations and Euler type dynamic equations are shown.",
address="Elsevier",
chapter="135851",
doi="10.1016/j.aml.2017.02.013",
howpublished="online",
institution="Elsevier",
number="73",
volume="2017",
year="2017",
month="april",
pages="84--90",
publisher="Elsevier",
type="journal article in Web of Science"
}
```