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DIBLÍK, J. CHUPÁČ, R. RŮŽIČKOVÁ, M.
Original Title
Existence of unbounded solutions of a linear homogenous system of differential equations with two delays
Type
journal article in Web of Science
Language
English
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.
Keywords
system of differential equations, unbounded solution, exponential solution, delay
Authors
DIBLÍK, J.; CHUPÁČ, R.; RŮŽIČKOVÁ, M.
RIV year
2014
Released
1. 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
State
United States of America
Pages from
2447
Pages to
2459
Pages count
13
URL
http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=10243
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", journal="DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B", year="2014", volume="19", number="2014", pages="2447--2459", doi="10.3934/dcdsb.2014.19.2447", issn="1531-3492", url="http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=10243" }