Publication detail

# Existence of unbounded solutions of a linear homogenous system of differential equations with two delays

DIBLÍK, J. CHUPÁČ, R. RŮŽIČKOVÁ, M.

Original Title

Existence of unbounded solutions of a linear homogenous system of differential equations with two delays

English Title

Existence of unbounded solutions of a linear homogenous system of differential equations with two delays

Type

journal article in Web of Science

Language

en

Original Abstract

Asymptotic behavior of solutions of a linear homogeneous system of differential equations with deviating arguments in the form \dot y(t)=\beta(t)\left[y(t-\delta)-y(t-\tau)\right] is discussed for t\to\infty. It is assumed that y is an n-dimensional column vector, n>1$is an integer, \delta,\tau\in{\mathbb{R}}, \tau>\delta>0 and \beta(t) is an n\times n matrix defined for t\geq t_{0}, t_{0}\in\mathbb{R}, and such that its elements are nonnegative, continuous functions and in every row of this matrix is each time at least one element nonzero. The existence of solutions in an exponential form under certain assumptions is proved. Sufficient conditions for the existence of unbounded solutions are derived. The estimations for a solution are given and the scalar case is discussed as well.

English abstract

Asymptotic behavior of solutions of a linear homogeneous system of differential equations with deviating arguments in the form \dot y(t)=\beta(t)\left[y(t-\delta)-y(t-\tau)\right] is discussed for t\to\infty. It is assumed that y is an n-dimensional column vector, n>1$is an integer, \delta,\tau\in{\mathbb{R}}, \tau>\delta>0 and \beta(t) is an n\times n matrix defined for t\geq t_{0}, t_{0}\in\mathbb{R}, and such that its elements are nonnegative, continuous functions and in every row of this matrix is each time at least one element nonzero. The existence of solutions in an exponential form under certain assumptions is proved. Sufficient conditions for the existence of unbounded solutions are derived. The estimations for a solution are given and the scalar case is discussed as well.

Keywords

system of differential equations, unbounded solution, exponential solution, delay

RIV year

2014

Released

01.10.2014

Publisher

Southwest Missouri State University

Location

AMER INST MATHEMATICAL SCIENCES, PO BOX 2604, SPRINGFIELD, MO 65801-2604 USA

ISBN

1531-3492

Periodical

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B

Year of study

19

Number

2014

State

US

Pages from

2447

Pages to

2459

Pages count

13

URL

Documents

BibTex

```
@article{BUT110162,
author="Josef {Diblík} and Radoslav {Chupáč} and Miroslava {Růžičková}",
title="Existence of unbounded solutions of a linear homogenous system of differential equations with two delays",
annote="Asymptotic behavior of solutions of a linear homogeneous system of differential equations with deviating arguments in the form \dot y(t)=\beta(t)\left[y(t-\delta)-y(t-\tau)\right] is discussed for t\to\infty. It is assumed that y is an n-dimensional column vector, n>1$is an integer, \delta,\tau\in{\mathbb{R}}, \tau>\delta>0 and \beta(t) is an n\times n matrix defined for t\geq t_{0}, t_{0}\in\mathbb{R}, and such that its elements are nonnegative, continuous functions and in every row of this matrix is each time at least one element nonzero. The existence of solutions in an exponential form under certain assumptions is proved. Sufficient conditions for the existence of unbounded solutions are derived. The estimations for a solution are given and the scalar case is discussed as well.",
address="Southwest Missouri State University",
chapter="110162",
doi="10.3934/dcdsb.2014.19.2447",
howpublished="online",
institution="Southwest Missouri State University",
number="2014",
volume="19",
year="2014",
month="october",
pages="2447--2459",
publisher="Southwest Missouri State University",
type="journal article in Web of Science"
}
```