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.

中文翻译：

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Banach空间中某些半线性发展方程的S-渐近Bloch型周期解

本文主要涉及S-渐近Bloch型周期。首先，我们引入了一个新的概念小号-asymptotically Bloch型周期函数，其可被看作是概念一般化小号-asymptotically ω为周期函数和小号-asymptotically ω -抗周期函数。其次，我们建立了S-渐近Bloch型周期函数的一些基本性质。最后，我们将获得的结果用于研究Banach空间中某些半线性微分方程的S渐近Bloch型周期温和解的存在性和唯一性。