Displaying similar documents to “On a boundary value problem for nonlinear functional differential equations.”

Nonnegative solutions of a class of second order nonlinear differential equations

S. Staněk (1992)

Annales Polonici Mathematici

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A differential equation of the form (q(t)k(u)u')' = λf(t)h(u)u' depending on the positive parameter λ is considered and nonnegative solutions u such that u(0) = 0, u(t) > 0 for t > 0 are studied. Some theorems about the existence, uniqueness and boundedness of solutions are given.

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.