The existence and uniqueness of periodic solutions for nonlinear neutral first order differential equation with functional delay - A. Makhzoum, Haitham; A. Elmansouri, Rafik (Libyan Journal of Science &Technology, 2022)
We employ the fixed point theorem of Krasnoselskii, to show the existence and uniqueness of periodic solutions of the nonlinear neutral differential equation: By modifying the given neutral differential equation into an equivalent integral equation using lemma (2.1). This is done by constructing appropriate operators, one is a contraction and the other is compact, which allow us to prove the existence of periodic solutions. In addition, we used the Banach fixed-point theorem to guarantee a unique periodic solution.