The Existence Of Asymptotically Almost Periodic Solutions And Pseudo Almost Periodic Solutions For A Class Of Complex Differential Equations

In this paper,we study the existence of asymptotically almost periodic solutions and pseudo almost periodic solutions to complex differential equation x'=?x+t),t ?R+by using coincidence degree theory and Schauder fixed point theory,where ? ? C,and ?(x,t)is a binary function mapped from set C × R+to set C.The primary coverage are as follows:In the first chapter,we introduce the development background of almost peri-odic function,asymptotically almost periodic function and pseudo almost periodic function,and study the almost periodic solutions of differential equations related to this paper.In the second chapter,we review the definition,properties and some important conclusions of almost periodic type functions,and characterize the norm relationship between almost periodic type functions and its original function.In the third chapter,we establish the criterion of compactness of asymptotically almost periodic function sets and pseudo almost periodic function sets.In the fourth chapter,we construct a kind of almost periodic function space,which makes the integral operator has certain compactness,and the existence of asymptotic almost periodic solutions and pseudo almost periodic solutions of com-plex differential equations is verified by Schauder fixed point theory and coincidence degree theory.