**
R. Hakl, A. Lomtatidze, J. Sremr**

##
Solvability and the Unique Solvability of a Periodic Type Boundary Value Problem
for First Order Scalar Functional Differential Equation

**abstract:**

Nonimprovable in a certain sense, sufficient conditions for the solvability
and unique solvability of the problem

u'(t) = F(u)(t), u(a) - lu(b) = h(u)

are established, where F: C([a,b]; R) --> L([a,b]; R) is a continuous operator
satisfying the Caratheodory condition, h: C([a,b]; R) --> R is a continuous
functional, and l in R_{+}.