On the existence and uniqueness of positive periodic solutions of neutral differential equations

Abstract

In this paper, we investigate a nonlinear neutral differential equation of first order with iterative terms and constant time delays. We obtain new results on the existence and uniqueness of positive periodic solutions of the nonlinear neutral differential equation such that the solution depends on the functions of that the nonlinear neutral differential equation. The proof of the new results depends on some fixed point theorems and the Green's functions. We also provide a numerical example to demonstrate the conditions of the new results can be satisfied and applied.