Detail publikace

# Asymptotic behavior of solutions of systems of dynamic equations on time scales in a set whose boundary is a combination of strict egress and strict ingress points

Originální název

Asymptotic behavior of solutions of systems of dynamic equations on time scales in a set whose boundary is a combination of strict egress and strict ingress points

Anglický název

Asymptotic behavior of solutions of systems of dynamic equations on time scales in a set whose boundary is a combination of strict egress and strict ingress points

Jazyk

en

Originální abstrakt

In this paper we study the asymptotic behavior of solutions of nonlinear dynamic systems on time scales of the form $$y^\Delta(t)=f(t,y(t)),$$ where $f\colon\mathbb{T}\times\mathbb{R}^n\rightarrow\mathbb{R}^n$ and $\mathbb{T}$ is a time scale. For a given set $\Omega\subset\mathbb{T}\times\mathbb{R}^{n}$, we formulate the conditions for function $f$, which guarantee that at least one solution $y$ of the above system stays in $\Omega$. The dimension of the space of initial data generating such solutions is discussed and perturbed linear systems are considered as well. A linear system with singularity at infinity is considered as an example.

Anglický abstrakt

In this paper we study the asymptotic behavior of solutions of nonlinear dynamic systems on time scales of the form $$y^\Delta(t)=f(t,y(t)),$$ where $f\colon\mathbb{T}\times\mathbb{R}^n\rightarrow\mathbb{R}^n$ and $\mathbb{T}$ is a time scale. For a given set $\Omega\subset\mathbb{T}\times\mathbb{R}^{n}$, we formulate the conditions for function $f$, which guarantee that at least one solution $y$ of the above system stays in $\Omega$. The dimension of the space of initial data generating such solutions is discussed and perturbed linear systems are considered as well. A linear system with singularity at infinity is considered as an example.

BibTex


@article{BUT107428,
author="Josef {Diblík} and Jiří {Vítovec}",
title="Asymptotic behavior of solutions of systems of dynamic equations on time scales in a set whose boundary is a combination of strict egress and strict ingress points",
annote="In this paper we study the asymptotic behavior of solutions of nonlinear dynamic systems on time scales of the form $$y^\Delta(t)=f(t,y(t)),$$ where
$f\colon\mathbb{T}\times\mathbb{R}^n\rightarrow\mathbb{R}^n$ and $\mathbb{T}$ is a time scale. For a given set $\Omega\subset\mathbb{T}\times\mathbb{R}^{n}$, we formulate the conditions for function $f$, which guarantee that at least one solution $y$ of the above system stays in $\Omega$. The dimension of the space of initial data generating such solutions is discussed and perturbed linear systems are considered as well. A linear system with singularity at infinity is considered as an example.",
chapter="107428",
doi="10.1016/j.amc.2014.04.021",
number="6",
volume="238",
year="2014",
month="june",
pages="289--299",
type="journal article in Web of Science"
}