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

0378921 - MÚ 2013 RIV US eng J - Journal Article
Domoshnitsky, A. - Hakl, Robert - Šremr, Jiří
Component-wise positivity of solutions to periodic boundary problem for linear functional differential system.
Journal of Inequalities and Applications. Roč. 112, May 22 (2012), s. 1-23. ISSN 1025-5834
Institutional support: RVO:67985840
Keywords : periodic problem * linear functional differential system * non-negative solution
Subject RIV: BA - General Mathematics
Impact factor: 0.879, year: 2010
http://www.journalofinequalitiesandapplications.com/content/2012/1/112

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.
Permanent Link: http://hdl.handle.net/11104/0210233