The authors are interested in the solvability of the functional differential equation \[ u''(t)-l(u)(t)-F(u)(t)= 0 \] with the boundary condtions \[ u(a) = 0 , u(b) = u(t_0),\quad t_0\in ]a,b[. \] They establish sufficient conditions for the solvability of such problem. As applications they consider differential equations with deviating argument and integro-differential equations.