Periodic solutions and attractiveness for some partial functional differential equations with lack of compactness

Ezzinbi, Khalil; Taoudi, Mohamed Aziz

doi:10.1090/proc/15313

Periodic solutions and attractiveness for some partial functional differential equations with lack of compactness
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by Khalil Ezzinbi and Mohamed Aziz Taoudi PDF

Proc. Amer. Math. Soc. 149 (2021), 1165-1174 Request permission

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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