Pseudo \(S\)-asymptotically Bloch type periodicity with applications to some evolution equations (Q2039385)

Summary: 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.