On a boundary value problem for scalar linear functional differential equations

R. Hakl, A. Lomtatidze and I. P. Stavroulakis

Abstract and Applied Analysis, 2004, vol. 2004, 1-23

Abstract:

Theorems on the Fredholm alternative and well-posedness of the linear boundary value problem u ′ ( t ) = ℓ ( u ) ( t ) + q ( t ) , h ( u ) = c , where ℓ : C ( [ a , b ] ; ℝ ) → L ( [ a , b ] ; ℝ ) and h : C ( [ a , b ] ; ℝ ) → ℝ are linear bounded operators, q ∈ L ( [ a , b ] ; ℝ ) , and c ∈ ℝ , are established even in the case when ℓ is not a strongly bounded operator. The question on the dimension of the solution space of the homogeneous equation u ′ ( t ) = ℓ ( u ) ( t ) is discussed as well.

Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:494856

DOI: 10.1155/S1085337504309061

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