Abstract
In this paper, we study the existence of periodic and nonnegative periodic solutions of the nonlinear neutral differential equation
x' (t) = -a (t) h (x (t - tau (t))) + c (t) x' (t - tau (t)) + G(t, x (t), x (t - tau (t))).
We invert this equation to construct a sum of a compact map and a large contraction which is suitable for applying the modification of Krasnoselskii's theorem. The Caratheodory condition is used for the function G.