Detail publikace

# Ohraničená řešení zpožděných dynamických rovnic na časových škálách

DIBLÍK, J. VÍTOVEC, J.

Originální název

Bounded solutions of delay dynamic equations on time scales

Český název

Ohraničená řešení zpožděných dynamických rovnic na časových škálách

Anglický název

Bounded solutions of delay dynamic equations on time scales

Typ

článek v časopise

Jazyk

en

Originální abstrakt

In this paper we discuss the asymptotic behavior of solutions of a delay dynamic equation $$y^{\Delta}(t)=f(t,y(\tau(t)))$$ where $f\colon\mathbb{T}\times\mathbb{R}\rightarrow\mathbb{R}$, \tau\colon\T\rightarrow \T$is a delay function and$\mathbb{T}$is a time scale. We formulate a principle which gives the guarantee that the graph of at least one solution of above mentioned equation stays in the prescribed domain. This principle uses the idea of the retraction method and is a suitable tool for investigating the asymptotic behavior of solutions of dynamic equations. This is illustrated by an example. Český abstrakt In this paper we discuss the asymptotic behavior of solutions of a delay dynamic equation $$y^{\Delta}(t)=f(t,y(\tau(t)))$$ where$f\colon\mathbb{T}\times\mathbb{R}\rightarrow\mathbb{R}$, \tau\colon\T\rightarrow \T$ is a delay function and $\mathbb{T}$ is a time scale. We formulate a principle which gives the guarantee that the graph of at least one solution of above mentioned equation stays in the prescribed domain. This principle uses the idea of the retraction method and is a suitable tool for investigating the asymptotic behavior of solutions of dynamic equations. This is illustrated by an example.

Anglický abstrakt

In this paper we discuss the asymptotic behavior of solutions of a delay dynamic equation $$y^{\Delta}(t)=f(t,y(\tau(t)))$$ where $f\colon\mathbb{T}\times\mathbb{R}\rightarrow\mathbb{R}$, \tau\colon\T\rightarrow \T$is a delay function and$\mathbb{T}$is a time scale. We formulate a principle which gives the guarantee that the graph of at least one solution of above mentioned equation stays in the prescribed domain. This principle uses the idea of the retraction method and is a suitable tool for investigating the asymptotic behavior of solutions of dynamic equations. This is illustrated by an example. Klíčová slova Asymptotic behavior, delay dynamic equation, time scale. Rok RIV 2012 Vydáno 24.10.2012 Nakladatel Springer Nature Strany od 1 Strany do 9 Strany počet 9 URL Plný text v Digitální knihovně BibTex  @article{BUT96019, author="Josef {Diblík} and Jiří {Vítovec}", title="Bounded solutions of delay dynamic equations on time scales", annote="In this paper we discuss the asymptotic behavior of solutions of a delay dynamic equation $$y^{\Delta}(t)=f(t,y(\tau(t)))$$ where$f\colon\mathbb{T}\times\mathbb{R}\rightarrow\mathbb{R}$, \tau\colon\T\rightarrow \T$ is a delay function and $\mathbb{T}$ is a time scale. We formulate a principle which gives the guarantee that the graph of at least one solution of above mentioned equation stays in
the prescribed domain. This principle uses the idea of the retraction method and is a suitable tool for investigating the asymptotic behavior of solutions of dynamic equations. This is illustrated by an example.",
address="Springer Nature",
chapter="96019",
doi="10.1186/1687-1847-2012-183",
institution="Springer Nature",
number="1",
volume="2012",
year="2012",
month="october",
pages="1--9",
publisher="Springer Nature",
type="journal article"
}