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

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26220%2F24%3APU151242" target="_blank" >RIV/00216305:26220/24:PU151242 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.sciencedirect.com/science/article/pii/S0893965924000521" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0893965924000521</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.aml.2024.109032" target="_blank" >10.1016/j.aml.2024.109032</a>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2024

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

APPLIED MATHEMATICS LETTERS

ISSN

1873-5452

e-ISSN

—

Svazek periodika

152

Číslo periodika v rámci svazku

June 2024

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

5

Strana od-do

1-5

Kód UT WoS článku

001197791100001

EID výsledku v databázi Scopus

2-s2.0-85185705410