Positive periodic solutions in neutral nonlinear differential equations

Abstract

We use Krasnoselskii's fixed point theorem to show that the nonlinear neutral differential equation with delay \begin{equation} \frac{d}{dt}[x(t) - ax(t-\tau)]= r(t)x(t)- f(t, x(t-\tau)) \end{equation} has a positive periodic solution. An example will be provided as an application to our theorems.