Existence And Uniqueness Of Positive Periodic Solutions For First-order Functional Differential Equations

In the first chapter, we introduce the development of functional differential equa-tions and describe the basic concepts.In the second chapter, we prove the existence and uniqueness of positive periodic solutions for first-order functional differential equation y’(t)=-a(t)y(t)+f(t, y(t-τ(t)))+g(t) under two different conditions, by using two fixed point theorems of general α—concave operators and homogeneous operators in ordered Banach spaces.In the first section of the third chapter, the existence and uniqueness of positive periodic solutions for first-order functional differential equation y’(t)=-a(t)y(t)+f(t, y(t-τ(t)))+g(t, y(t-τ(t))) was established by using a fixed point theorem of a sum operator.In the second section of the third chapter, we study the existence and uniqueness of positive periodic solutions for first-order functional differential equation y’(t)=-a(t)y(t)+λf1(t,y（t-τ(t)))+λf2(t,y(t-τ(t))). Our analysis relies on a fixed point theorem for mixed monotone operators.In the last section of the third chapter, by means of a fixed point theorem in partially ordered sets, we consider the existence and uniqueness of positive periodic solutions for the following y’(t)＝-a(t)y(t)+f(t, y(t-τ(t))).