Publication 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
Type
journal article in Web of Science
Language
English
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.
Keywords
Positive solution; Asymptotic behavior; Delayed equations; Multiple delays; First integral
Authors
DIBLÍK, J.
Released
3. 6. 2024
Publisher
PERGAMON-ELSEVIER SCIENCE LTD
Location
OXFORD
ISBN
1873-5452
Periodical
APPLIED MATHEMATICS LETTERS
Year of study
152
Number
June 2024
State
United States of America
Pages from
1
Pages to
5
Pages count
5
URL
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="1873-5452",
url="https://www.sciencedirect.com/science/article/pii/S0893965924000521"
}