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Component-wise positivity of solutions to periodic boundary problem for linear functional differential system
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SYSNO ASEP 0378921 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Component-wise positivity of solutions to periodic boundary problem for linear functional differential system Author(s) Domoshnitsky, A. (IL)
Hakl, Robert (MU-W) RID, SAI, ORCID
Šremr, Jiří (MU-W) RID, SAI, ORCIDSource Title Journal of Inequalities and Applications - ISSN 1025-5834
Roč. 112, May 22 (2012), s. 1-23Number of pages 23 s. Language eng - English Country US - United States Keywords periodic problem ; linear functional differential system ; non-negative solution Subject RIV BA - General Mathematics Institutional support MU-W - RVO:67985840 UT WOS 000317835000001 EID SCOPUS 84870470563 DOI 10.1186/1029-242X-2012-112 Annotation 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. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2013
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