Asymptotically Almost Periodic Solutions And Asymptotically Almost Automorphic Solutions For Two Classes Of Semilinear Differential Equations

Ever since the almost periodic functions were proposed,it attracted to the eyes of many scholars,so that they discussed it deeply.After that,numerous mathematician put forward and researched asymptotically almost periodic functions deeply and all kinds almost automorphic type functions gradually.In addition,many almost periodic type functions and almost automorphic type functions appeared in mathematics,physics and other fields.The most common is that almost periodic type functions and almost automorphic type functions are applyed to all kinds integral equations,differential equations and partial differential equations.And for that,the point is that explore the causes of almost periodic type solutions and almost automorphic type solutions of a great variety functions.In the midst of it all,it is very popular with scholars in difference equations field,the research scope is more extensive.So,asymptotically almost periodic solutions and asymptotically almost automorphic solutions of two classes seimilinear differential equations will be the key points in this paper.Then,the key points of this paper are as follows:Primarily,the existence and uniqueness of that asymptotically almost periodic solution of a class differential equation with variable delays was discussed in the research.Banach fixed point theorem and uniform continuity of functions will be used in proof process,and asymptotically almost periodic functions relevant theories will be combined.Before certification,relevant definitions of almost periodic functions and asymptotically almost periodic functions will be introduced.The translation problem and composite problem of asymptotically almost periodic functions also need to be proposed.To explore the existence and uniqueness of asymptotically almost periodic functions after all conditions are given.Secondly,the existence and uniqueness of asymptotically almost automorphic solutions on another class of semilinear differential equation will be discussed.In the same way,relevant definitions of almost automorphic functions and asymptotically almost automorphic functions will be recommded,then the research process will be mainly combined with Banach fixed pointed theorem and Lebesgue control convergence theorem.