Displaying similar documents to “On one class of solvable boundary value problems for ordinary differential equation of n -th order”

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...