Displaying similar documents to “On effective criteria of solvability of the boundary value problems for ordinary differential equations of the n -th order”

On four-point boundary value problem without growth conditions

Irena Rachůnková (1999)

Czechoslovak Mathematical Journal

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We prove the existence of solutions of four-point boundary value problems under the assumption that f fulfils various combinations of sign conditions and no growth restrictions are imposed on f . In contrast to earlier works all our results are proved for the Carathéodory case.

On an antiperiodic type boundary value problem for first order linear functional differential equations

Robert Hakl, Alexander Lomtatidze, Jiří Šremr (2002)

Archivum Mathematicum

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Nonimprovable, in a certain sense, sufficient conditions for the unique solvability of the boundary value problem u ' ( t ) = ℓ ( u ) ( t ) + q ( t ) , u ( a ) + λ u ( b ) = c are established, where ℓ : C ( [ a , b ] ; R ) → L ( [ a , b ] ; R ) is a linear bounded operator, q ∈ L ( [ a , b ] ; R ) , λ ∈ R + , and c ∈ R . The question on the dimension of the solution space of the homogeneous problem u ' ( t ) = ℓ ( u ) ( t ) , u ( a ) + λ u ( b ) = 0 is discussed as well.