Periodicity and non‐negativity of solutions for nonlinear neutral differential equations with variable delay via fixed point theorems

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 delayx ′t = − a t h x t − τ t+ c tx ′t − τ t+ G t , x t , x t − τ 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 © 2015 John Wiley & Sons, Ltd.