Displaying similar documents to “Differential inequalities for one component of solution vector for systems of linear functional differential equations.”

Positivity of Green's matrix of nonlocal boundary value problems

Alexander Domoshnitsky (2014)

Mathematica Bohemica

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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 n i x i - j = 1 n m i j x j = β i , i = 1 , , n , where n i and m i j are linear bounded “local” and “nonlocal“ functionals, respectively, from the space of absolutely continuous functions. For instance, n i x i = x i ( ω ) or n i x i = x i ( 0 ) - x i ( ω ) and m i j x j = 0 ω k ( s ) x j ( s ) d s + r = 1 n i j c i j r x j ( t i j r ) can be considered. It is demonstrated that the positivity of Green’s operator of nonlocal problem follows from the positivity...