Dichotomy Condition and Periodic Solutions for Two Nonlinear Neutral Systems

Abstract

In this article, we consider two nonlinear neutral systems with multiple delays. Our main tool here is to use dichotomy theory to construct an implicit solution for these two systems. Utilizing Krasnoselskii’s fixed point theorem, we obtain sufficient criteria for the existence of periodic solutions, as well as for the uniqueness of solutions. The main results expand and generalize certain previously published findings.