Global properties of all maximal solutions of the iterative functional differential equation $x''(t)=a[x(x(t))-x(t)]+1$ are considered. Using a correspondence among solutions of the above equation and those of the functional differential equation $y'(t)=ay(t- by(t)$), global properties of all maximal solutions of the last equation are described.
"On global properties of solutions of the equation $y'(t)=ay(t-by(t))$." Hokkaido Math. J. 30 (1) 75 - 89, February 2001. https://doi.org/10.14492/hokmj/1350911924