ABSTRACT
This paper studies -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
-periodic solutions of homogeneous and inhomogeneous systems. Fixed-point theorems are used to show existence and uniqueness of
-periodic solutions of the nonlinear systems and examples are given to illustrate the theoretical results.
2010 Mathematics Subject Classification:
Acknowledgments
The authors are grateful to the referees for their careful reading of the manuscript and their valuable comments.
Disclosure statement
No potential conflict of interest was reported by the author(s).