Existence Of Almost Periodic And Almost Automorphic Solutions For Semilinear Functional Evolution Equations

By using a fixed point theorem and theory of integral semigroup, we have discussed the existence of pseudo almost periodic and asymptotically almost automorphic solutions for two classes of semilinear functional evolution equations. The whole dissertation contains three chapters.Chapter 1 is the introduction section, where we introduced the research background, our main work in this dissertation, and the fundamental definitions, signals and basic theory about integral semigroup, which will be used in this dissertation. In Chapter 2, we studied the existence of pseudo almost periodic solutions for a class of semilinear neutral functional evolution equations with the non-densely defined domain, and an example was given to show the application of the obtained theorem. In Chapter 3, we discussed the existence of asymptotically almost automorphic solutions for a class of non-densely defined neutral functional differential system with nonlocal conditions. And an example was also provided at last.