Existence, uniqueness, and continuous dependence on parameters of periodic solutions for a second-order neutral iterative differential equation

Abstract

This paper investigates a class of second-order neutral iterative differential equations. Using a hybrid analytical approach that combines the Krasnoselskii fixed point theorem, the Banach fixed point theorem, and the Green's function technique, we establish new sufficient conditions that guarantee the existence, uniqueness, and continuous dependence on parameters of periodic solutions. To demonstrate the applicability and effectiveness of the theoretical results, two illustrative examples are provided. In conclusion, the findings presented in this work extend and complement several existing contributions in the literature.