Positivity of green’s matrix of nonlocal boundary value problems

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We propose an approach for studying positivity of Green’s operators of a nonlocal boundary value problem for the system of n linear functional differential equations with the boundary conditions nixi − Σnj=1 mijxj = βi, i = 1,...,n, where ni and mij are linear bounded “local” and “nonlocal” functionals, respectively, from the space of absolutely continuous functions. For instance, (Formula presented.) can be considered. It is demonstrated that the positivity of Green’s operator of nonlocal problem follows from the positivity of Green’s operator for auxiliary “local” problem which consists of a “close” equation and the local conditions nixi = αi, i = 1,...,n.

Original languageEnglish
Pages (from-to)621-638
Number of pages18
JournalMathematica Bohemica
Issue number4
StatePublished - 2014


  • Differential inequalities
  • Functional differential equation
  • Fundamental matrix
  • Nonlocal boundary value problem
  • Positivity of Green’s operator

All Science Journal Classification (ASJC) codes

  • Mathematics(all)


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