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

ABSTRACT

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

Keywords:

• Non-instantaneous impulsive differential systems
• $(\omega ,c)$-periodic solutions
• existence and uniqueness

2010 Mathematics Subject Classification:

• 34A34

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).

Additional information

Funding

This work is partially supported by the National Natural Science Foundation of China (11661016), Guizhou DataDriven Modeling Learning and Optimization Innovation Team ([2020]5016), Youth Development Project of GuizhouProvincial Education Department ([2021]266), Science and Technology Foundation of Guizhou Province ([2020]1Y002),Academic Seedling Cultivation and Innovation Exploration Special Cultivation Project Plan: GZLGXM-17, Postgraduate Education Innovation Program in Guizhou Province [YJSCXJH(2019)030], the Slovak Research and Development Agency under the contract No. APVV-18-0308, and the Slovak Grant Agency VEGA No. 1/0358/20 and No.2/0127/20.