Existence of asymptotically periodic solutions of partial functional differential equations with state-dependent delay. Issue 14 (26th October 2021)

• Record Type: Journal Article
• Authors: Andrade, Filipe; Cuevas, Claudio; Henríquez, Hernán R.
• Is Part Of: Applicable analysis. Volume 100:Issue 14(2021)
• Page Start: 2965
• Page End: 2988
• Publication Date: 2021-10-26
• Subjects: Retarded functional differential equations -- abstract functional differential equations -- equations with state-dependent delay -- mild solutions -- asymptotically periodic solutions; Primary: 34K30 -- 34K13 -- Secondary: 34G20; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2019.1704737
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: In this paper, we are concerned with systems determined by partial differential equations with infinite and state-dependent delay. To study the system, we model the equation as an abstract retarded functional differential equations with infinite and state-dependent delay. We establish the existence of mild solutions, and the existence of S-asymptotically periodic solutions and asymptotically periodic solutions using local Lipschitz conditions on the involved functions. We apply our results to study the existence of asymptotically periodic solutions of a partial differential equation with infinite and state-dependent delay.