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Publication detail
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
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
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="1873-5452", url="https://www.sciencedirect.com/science/article/pii/S0893965924000521" }