Solvability of inhomogeneous autonomous differential equation with aftereffect on the negative semi-axis

We obtain necessary and sufficient condition of solvability for a linear autonomous inhomogeneous functional differential equation with aftereffect and find the representation of all solutions in the special space of integrable functions with exponential weight. The obtained results are applied for study of two inhomogeneous differential equations with delay (the first equation is with concentrated delay, and the second one is with distributed delay). We give effective description of the space of solutions for these equations.