Abstract:This paper deals with the existence of periodic solutions and attractiveness for some partial functional differential equations in Banach spaces. We assume that the first linear part generates a strongly continuous semigroup, while the delayed part is periodic with respect to the first argument. We prove that the existence of a bounded solution implies the existence of a periodic solution. Several results regarding uniqueness and global attractiveness of periodic solutions are also established. The analysis relies on a fixed point theorem of Chow and Hale's type and uses some arguments of weak topology. Our theorems extend in a broad sense some new and classical related results. An application to a transport equation with delay is also presented.

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中文翻译：

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缺乏紧性的某些偏泛函微分方程的周期解和吸引性

摘要：本文讨论了Banach空间中某些偏泛函微分方程周期解的存在性和吸引性。我们假设第一线性部分生成一个强连续半群，而延迟部分相对于第一个参数是周期性的。我们证明有界解的存在意味着周期解的存在。还建立了关于周期解的唯一性和全局吸引力的几个结果。该分析基于Chow和Hale类型的不动点定理，并使用了一些弱拓扑参数。我们的定理在广义上扩展了一些新的和经典的相关结果。还提出了具有时滞的输运方程的应用。

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