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Kernel Sections and (Almost) Periodic Solutions for a Class of Partial Functional Differential Equations

Xiang Li, Zhixiang Li

Abstract


In this paper, we investigate the long time behavior of a nonautonomous partial functional differential equation with finite delay, whose linear part is not necessarily densely defined but satisfies Hille-Yosida condition. First we obtain the existence of compact kernel sections. Then we prove the kernel has only one complete trajectory. As the corollary, we obtain the (almost) periodic solution attracts all solutions exponentially provided the time dependent term is (almost) periodic with respect to time t.

Keywords


kernel section, partial functional differential equation, complete trajectory, periodic solution, almost periodic solution.

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