Open Access Open Access  Restricted Access Subscription or Fee Access

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

Xiang Li, Zhixiang Li


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.


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

Full Text:


Disclaimer/Regarding indexing issue:

We have provided the online access of all issues and papers to the indexing agencies (as given on journal web site). It’s depend on indexing agencies when, how and what manner they can index or not. Hence, we like to inform that on the basis of earlier indexing, we can’t predict the today or future indexing policy of third party (i.e. indexing agencies) as they have right to discontinue any journal at any time without prior information to the journal. So, please neither sends any question nor expects any answer from us on the behalf of third party i.e. indexing agencies.Hence, we will not issue any certificate or letter for indexing issue. Our role is just to provide the online access to them. So we do properly this and one can visit indexing agencies website to get the authentic information. Also: DOI is paid service which provided by a third party. We never mentioned that we go for this for our any journal. However, journal have no objection if author go directly for this paid DOI service.