Existence Of Asymptotically Almost Automorphic Solutions And S-asymptotically Periodic Type Solutions For Two Kinds Of Difference Equations

In this paper,we mainly study the existence of asymptotically almost automorphic solutions,S-asymptotically w-periodic solutions and pseudo S-asymptotically w-periodic solutions for two type of difference equations.Specifically there are the following sections.In the first chapter,we introduce the historical development of almost periodic type functions and S-asymptotically periodic type functions.In the second chapter,we introduce the definitions and properties of almost periodic functions,almost automorphic functions,asymptotically almost automorphic functions,S-asymptotically w-periodic functions and pseudo S-asymptotically w-periodic functions.In the third chapter,we use the Leray-Schauder alternative theorem,to prove the existence of asymptotically almost automorphic solutions of the Volterra-type difference equation:(?)In the fourth chapter,we use the convex cone theory to study the existence of S-asymptotically w-periodic solutions and pseudo S-asymptotically w-periodic solutions of the difference equation(?).