Component-wise positivity of solutions to periodic boundary problem for linear functional differential system

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F12%3A00378921" target="_blank" >RIV/67985840:_____/12:00378921 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1186/1029-242X-2012-112" target="_blank" >http://dx.doi.org/10.1186/1029-242X-2012-112</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1186/1029-242X-2012-112" target="_blank" >10.1186/1029-242X-2012-112</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Component-wise positivity of solutions to periodic boundary problem for linear functional differential system

Popis výsledku v původním jazyce

The classical Ważewski theorem claims that the non-negativity of non-diagonal coefficients is necessary and sufficient for non-negativity of all the components of solution vector to a system of linear differential inequalities of the first order. Although this result was extended on various boundary value problems and on delay differential systems, analogs of these heavy restrictions on non-diagonal coefficients preserve in all assertions of this sort. It is clear from formulas of the integral representation of the general solution that these theorems claim actually the positivity of all elements of Green?s matrix. The method to compare only one component of the solution vector, which does not require such heavy restrictions, is proposed in this article. Note that comparison of only one component of the solution vector means the positivity of elements in a corresponding row of Green?s matrix.

Název v anglickém jazyce

Component-wise positivity of solutions to periodic boundary problem for linear functional differential system

Popis výsledku anglicky

The classical Ważewski theorem claims that the non-negativity of non-diagonal coefficients is necessary and sufficient for non-negativity of all the components of solution vector to a system of linear differential inequalities of the first order. Although this result was extended on various boundary value problems and on delay differential systems, analogs of these heavy restrictions on non-diagonal coefficients preserve in all assertions of this sort. It is clear from formulas of the integral representation of the general solution that these theorems claim actually the positivity of all elements of Green?s matrix. The method to compare only one component of the solution vector, which does not require such heavy restrictions, is proposed in this article. Note that comparison of only one component of the solution vector means the positivity of elements in a corresponding row of Green?s matrix.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2012

Kód důvěrnosti údajů

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

Název periodika

Journal of Inequalities and Applications

ISSN

1025-5834

e-ISSN

—

Svazek periodika

112

Číslo periodika v rámci svazku

May 22

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

23

Strana od-do

1-23

Kód UT WoS článku

000317835000001

EID výsledku v databázi Scopus

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