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Periodic solutions and attractiveness for some partial functional differential equations with lack of compactness.
- Source :
-
Proceedings of the American Mathematical Society . Mar2021, Vol. 149 Issue 3, p1165-1174. 10p. - Publication Year :
- 2021
-
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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00029939
- Volume :
- 149
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Proceedings of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 148558572
- Full Text :
- https://doi.org/10.1090/proc/15313