Abstract
We use a modification of Krasnoselskii's fixed point theorem introduced by Burton to show the periodicity and non-negativity of solutions for the nonlinear neutral differential equation with variable delay
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 the sum of a compact map and a large contraction, which is suitable for applying the modification of Krasnoselskii's theorem. Copyright (C) 2015 John Wiley & Sons, Ltd.