Displaying similar documents to “Positivity of Green's matrix of nonlocal boundary value problems”

On solvability sets of boundary value problems for linear functional differential equations

Eugene Bravyi (2011)

Mathematica Bohemica

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Consider boundary value problems for a functional differential equation x ( n ) ( t ) = ( T + x ) ( t ) - ( T - x ) ( t ) + f ( t ) , t [ a , b ] , l x = c , where T + , T - : 𝐂 [ a , b ] 𝐋 [ a , b ] are positive linear operators; l : 𝐀𝐂 n - 1 [ a , b ] n is a linear bounded vector-functional, f 𝐋 [ a , b ] , c n , n 2 . Let the solvability set be the set of all points ( 𝒯 + , 𝒯 - ) 2 + such that for all operators T + , T - with T ± 𝐂 𝐋 = 𝒯 ± the problems have a unique solution for every f and c . A method of finding the solvability sets are proposed. Some new properties of these sets are obtained in various cases. We continue the investigations of the solvability sets started...

Existence of a positive solution to a nonlocal semipositone boundary value problem on a time scale

Christopher S. Goodrich (2013)

Commentationes Mathematicae Universitatis Carolinae

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We consider the existence of at least one positive solution to the dynamic boundary value problem - y Δ Δ ( t ) = λ f ( t , y ( t ) ) , t [ 0 , T ] 𝕋 y ( 0 ) = τ 1 τ 2 F 1 ( s , y ( s ) ) Δ s y σ 2 ( T ) = τ 3 τ 4 F 2 ( s , y ( s ) ) Δ s , where 𝕋 is an arbitrary time scale with 0 < τ 1 < τ 2 < σ 2 ( T ) and 0 < τ 3 < τ 4 < σ 2 ( T ) satisfying τ 1 , τ 2 , τ 3 , τ 4 𝕋 , and where the boundary conditions at t = 0 and t = σ 2 ( T ) can be both nonlinear and nonlocal. This extends some recent results on second-order semipositone dynamic boundary value problems, and we illustrate these extensions with some examples.

On a class of m -point boundary value problems

Rodica Luca (2012)

Mathematica Bohemica

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We investigate the existence of positive solutions for a nonlinear second-order differential system subject to some m -point boundary conditions. The nonexistence of positive solutions is also studied.