Electronic Journal of Differential Equations, Vol. 2010(2010), No. 88, pp. 1-8. Title: A nonlinear neutral periodic differential equation Author: Eric R. Kaufmann (Un. of Arkansas, Little Rock, AR, USA) Abstract: In this article we consider the existence, uniqueness and positivity of a first order non-linear periodic differential equation. The main tool employed is the Krasnosel'skii's fixed point theorem for the sum of a completely continuous operator and a contraction. Submitted March 22, 2010. Published June 25, 2010. Math Subject Classifications: 34A37, 34A12, 39A05. Key Words: Fixed point theory; nonlinear dynamic equation; periodic.