Detail publikačního výsledku

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

ŘEHÁK, P.

Originální název

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

Anglický název

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

Druh

Článek WoS

Originální abstrakt

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.

Anglický abstrakt

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.

Klíčová slova

higher order dynamic equation; time scale; asymptotic equivalence

Klíčová slova v angličtině

higher order dynamic equation; time scale; asymptotic equivalence

Autoři

ŘEHÁK, P.

Rok RIV

2018

Vydáno

23.04.2017

Nakladatel

Elsevier

ISSN

0893-9659

Periodikum

Applied Mathematics Letters

Svazek

2017

Číslo

73

Stát

Spojené státy americké

Strany od

84

Strany do

90

Strany počet

7

URL

http://www.sciencedirect.com/science/article/pii/S0893965917300502

BibTex

@article{BUT135851,
  author="Pavel {Řehák}",
  title="On asymptotic relationships between two higher order dynamic equations on time scales",
  journal="Applied Mathematics Letters",
  year="2017",
  volume="2017",
  number="73",
  pages="84--90",
  doi="10.1016/j.aml.2017.02.013",
  issn="0893-9659",
  url="http://www.sciencedirect.com/science/article/pii/S0893965917300502"
}