On an antiperiodic type boundary value problem for first order linear functional differential equations. (English) Zbl 1087.34042

Hakl, R.; Lomtatidze, A.; Šremr, J.

Arch. Math., Brno 38, No. 2, 149-160 (2002).

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

Keywords:

linear functional differential equation; antiperiodic type BVP; solvability and unique solvability