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, issue 1, 45-67

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:wly:jnlaaa:v:2004:y:2004:i:1:p:45-67

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