Existence and Uniqueness of Periodic Solutions of Mixed Monotone Functional Differential Equations

Abstract

This paper deals with the existence and uniqueness of periodic solutions for the first-order functional differential equation $y^{\prime }\left(t\right)=-a\left(t\right)y\left(t\right)+f_1\left(t,y\left(t-\tau \left(t\right)\right)\right)+f_2\left(t,y\left(t-\tau \left(t\right)\right)\right)$ with periodic coefficients and delays. We choose the mixed monotone operator theory to approach our problem because such methods, besides providing the usual existence results, may also sometimes provide uniqueness as well as additional numerical schemes for the computation of solutions.