Detail publikace

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

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

Jazyk

en

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.

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.",
}