(ω, c)-periodic solutions for time-varying non-instantaneous impulsive differential systems. Issue 15 (13th October 2022)

• Record Type: Journal Article
• Authors: Liu, Kui; Fečkan, Michal; O'Regan, Donal; Wang, JinRong
• Is Part Of: Applicable analysis. Volume 101:Issue 15(2022)
• Page Start: 5469
• Page End: 5489
• Publication Date: 2022-10-13
• Subjects: Non-instantaneous impulsive differential systems -- (ω, c)-periodic solutions -- existence and uniqueness; 34A34; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2021.1895123
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: This paper studies ( ω, c ) -periodic solutions for time-varying non-instantaneous impulsive differential equations. The Cauchy matrix of the time-varying linear non-instantaneous impulsive system is constructed and some basic properties are derived. The method of constant variations and the adjoint matrix are used to find sufficient and necessary conditions for ( ω, c ) -periodic solutions of homogeneous and inhomogeneous systems. Fixed-point theorems are used to show existence and uniqueness of ( ω, c ) -periodic solutions of the nonlinear systems and examples are given to illustrate the theoretical results.