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On an antiperiodic type boundary value problem for first order linear functional differential equations. (English) Zbl 1087.34042
Summary: Nonimprovable, in a certain sense, sufficient conditions for the unique solvability of the boundary value problem $u' (t) = \ell (u) (t) + q (t), \qquad u (a) + \lambda u (b) = c$ are established, where $$\ell : C([a, b]; \mathbb R) \to L([a, b]; \mathbb R)$$ is a linear bounded operator, $$q \in L([a, b]; \mathbb R)$$, $$\lambda \in \mathbb R_+$$, and $$c \in \mathbb R$$. The problem of the dimension of the solution space of the homogeneous problem $u' (t) = \ell (u) (t), \qquad u (a) + \lambda u (b) = 0$ is discussed.

MSC:
 34K10 Boundary value problems for functional-differential equations 34K13 Periodic solutions to functional-differential equations
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