Publication result detail

Novel criterion for the existence of solutions with positive coordinates to a system of linear delayed differential equations with multiple delays

DIBLÍK, J.

Original Title

Novel criterion for the existence of solutions with positive coordinates to a system of linear delayed differential equations with multiple delays

English Title

Novel criterion for the existence of solutions with positive coordinates to a system of linear delayed differential equations with multiple delays

Type

WoS Article

Original Abstract

A linear system of delayed differential equations with multiple delays x(t) = - Sigma(s)(t=1) c(i)(t)A(i)(t)x(t-tau(i)(t)), t is an element of[t(0), infinity), is considered where x is an n-dimensional column vector, t(0) is an element of R, s is a fixed integer, delays tau(i) are positive and bounded, entries of n by n matrices A(i) as well as functions c(i) are nonnegative, and the sums of columns of the matrix A(i) (t) are identical and equal to a function alpha(i)(t). It is proved that, on [t(0), infinity), the system has a solution with positive coordinates if and only if the scalar equation y(t) = - Sigma(s)(t=1) c(i)(t)A(i)(t)y(t-tau(i)(t)), t is an element of[t(0), infinity), has a positive solution. Some asymptotic properties of solutions related to both equations are also discussed. Illustrative examples are considered and some open problems formulated.

English abstract

A linear system of delayed differential equations with multiple delays x(t) = - Sigma(s)(t=1) c(i)(t)A(i)(t)x(t-tau(i)(t)), t is an element of[t(0), infinity), is considered where x is an n-dimensional column vector, t(0) is an element of R, s is a fixed integer, delays tau(i) are positive and bounded, entries of n by n matrices A(i) as well as functions c(i) are nonnegative, and the sums of columns of the matrix A(i) (t) are identical and equal to a function alpha(i)(t). It is proved that, on [t(0), infinity), the system has a solution with positive coordinates if and only if the scalar equation y(t) = - Sigma(s)(t=1) c(i)(t)A(i)(t)y(t-tau(i)(t)), t is an element of[t(0), infinity), has a positive solution. Some asymptotic properties of solutions related to both equations are also discussed. Illustrative examples are considered and some open problems formulated.

Keywords

Positive solution; Asymptotic behavior; Delayed equations; Multiple delays; First integral

Key words in English

Positive solution; Asymptotic behavior; Delayed equations; Multiple delays; First integral

Authors

DIBLÍK, J.

RIV year

2025

Released

03.06.2024

Publisher

PERGAMON-ELSEVIER SCIENCE LTD

Location

OXFORD

ISBN

1873-5452

Periodical

Applied Mathematics Letters

Volume

152

Number

June 2024

State

United States of America

Pages from

1

Pages to

5

Pages count

5

URL

https://www.sciencedirect.com/science/article/pii/S0893965924000521

BibTex

@article{BUT188485,
  author="Josef {Diblík}",
  title="Novel criterion for the existence of solutions with positive coordinates to a system of linear delayed differential equations with multiple delays",
  journal="Applied Mathematics Letters",
  year="2024",
  volume="152",
  number="June 2024",
  pages="1--5",
  doi="10.1016/j.aml.2024.109032",
  issn="0893-9659",
  url="https://www.sciencedirect.com/science/article/pii/S0893965924000521"
}