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  • 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.
  • 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. (en)
Title
  • Component-wise positivity of solutions to periodic boundary problem for linear functional differential system
  • Component-wise positivity of solutions to periodic boundary problem for linear functional differential system (en)
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  • Component-wise positivity of solutions to periodic boundary problem for linear functional differential system
  • Component-wise positivity of solutions to periodic boundary problem for linear functional differential system (en)
skos:notation
  • RIV/67985840:_____/12:00378921!RIV13-AV0-67985840
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  • I
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  • May 22
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  • 128216
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  • RIV/67985840:_____/12:00378921
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  • periodic problem; linear functional differential system; non-negative solution (en)
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  • US - Spojené státy americké
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  • [71C1A6470AFF]
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  • Journal of Inequalities and Applications
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  • 112
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  • Hakl, Robert
  • Domoshnitsky, A.
  • Šremr, Jiří
http://linked.open...ain/vavai/riv/wos
  • 000317835000001
issn
  • 1025-5834
number of pages
http://bibframe.org/vocab/doi
  • 10.1186/1029-242X-2012-112
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