(ω,c)-periodic solutions for time-varying non-instantaneous impulsive differential systems

This paper studies (Formula presented.) -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 (Formula presented.) -periodic solutions of homogeneous and inhomogeneous systems. Fixed-point theorems are used to show existence and uniqueness of (Formula presented.) -periodic solutions of the nonlinear systems and examples are given to illustrate the theoretical results.