The Existence of Periodic Solutions of Delay Differential Equations by E+-Conley Index Theory. (20th April 2022)

• Record Type: Journal Article
• Authors: Xiao, Huafeng
• Other Names: Rubbioni Paola Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2022(2022)
• Publication Date: 2022-04-20
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2022/3396716
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : In this paper, the E + -Conley index theory has been used to study the existence of periodic solutions of nonautonomous delay differential equations (in short, DDEs). The variational structure for DDEs is built, and the existence of periodic solutions of DDEs is transferred to that of critical points of the associated function. When DDEs are 2 π -nonresonant, some sufficient conditions are obtained to guarantee the existence of periodic solutions. When the system is 2 π -resonant at infinity, by making use a second disturbing of the original functional, some sufficient conditions are obtained to guarantee the existence of periodic solutions to DDEs.