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"
}