(ω, c)-periodic solutions for time-varying non-instantaneous impulsive differential systems. Issue 15 (13th October 2022) - Liu, Kui; Fečkan, Michal; O'Regan, Donal; Wang, JinRong
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.