Abstract
This paper is mainly concerned with the S-asymptotically Bloch type periodicity. Firstly, we introduce a new notion of S-asymptotically Bloch type periodic functions, which can be seen as a generalization of concepts of S-asymptotically ω-periodic functions and S-asymptotically ω-anti-periodic functions. Secondly, we establish some fundamental properties on S-asymptotically Bloch type periodic functions. Finally, we apply the results obtained to investigate the existence and uniqueness of S-asymptotically Bloch type periodic mild solutions to some semi-linear differential equations in Banach spaces.
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