On a boundary value problem for nonlinear functional differential equations.

Hakl, Robert

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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 $ℓ : C ([a, b]; R) \to L ([a, b]; R)$ is a linear bounded operator, $q \in L ([a, b]; R)$ , $λ \in R_{+}$ , and $c \in R$ . 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.

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