Existence of periodic or nonnegative periodic solutions for totally nonlinear neutral differential equations with infinite delay.

In this work, we investigate the existence of periodic or nonnegative periodic solutions for a totally nonlinear neutral differential equation with infinite delay. In the process, we convert the given neutral differential equation into an equivalent integral equation. Then, we employ Krasnoselski˘ı-Burton’s fixed point theorem to prove the existence of periodic or nonnegative periodic solutions. Two examples are provided to illustrate the obtained results. [ABSTRACT FROM AUTHOR]