Periodic Solutions For Neutral Functional Differential Equations

The functional differential equation is a very important kind of differential equations,which is widely used in biology,economics,genetics,medicine and many other fields.The related problem of periodic solutions for neutral functional differential equations is one of the hot issues in the fields of functional differential equations.The paper mainly studies the existence of periodic solutions for three kinds of neutral functional differential equation(system)by using fixed point theorems.For the first kind of equation,some sufficient conditions for the existence of nontrivial periodic solutions are obtained by using Schauder fixed point theorem and Contraction mapping theorem,and the existence result of unique periodic solutions is established;for the second kind of equation,some existence theorems of positive periodic solutions or negative periodic solutions are obtained by fixed point theorem on cone;for the third kind of equation,some sufficient conditions for the existence of positive periodic solutions are obtained by using Krasnoselskii fixed point theorem.