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₊.