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

Abstract

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.