Detail publikace

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

DIBLÍK, J. CHUPÁČ, R. RŮŽIČKOVÁ, M.

Originální název

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

Typ

článek v časopise ve Web of Science, Jimp

Jazyk

angličtina

Originální abstrakt

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.

Klíčová slova

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

Autoři

DIBLÍK, J.; CHUPÁČ, R.; RŮŽIČKOVÁ, M.

Rok RIV

2014

Vydáno

1. 10. 2014

Nakladatel

Southwest Missouri State University

Místo

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

ISSN

1531-3492

Periodikum

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B

Ročník

19

Číslo

2014

Stát

Spojené státy americké

Strany od

2447

Strany do

2459

Strany počet

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"
}