Pseudo S-Asymptotically Bloch Type Periodicity with Applications to Some Evolution Equations

This paper is mainly focused upon the pseudo S -asymptotically Bloch type periodicity and its applications. Firstly, a new notion of pseudo S -asymptotically Bloch type periodic functions is introduced, and some fundamental properties on pseudo S -asymptotically Bloch type periodic functions are established. Then, the notion and properties of weighted pseudo S -asymptotically Bloch type periodic functions are similarly presented. Finally, the obtained results are applied to investigate the existence and uniqueness of pseudo S -asymptotically Bloch type periodic mild solutions for some semi-linear evolution equations in Banach spaces.