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.

中文翻译：

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(ω , c)-时变非瞬时脉冲微分系统的周期解

摘要

本文研究$(\omega ,C)$-时变非瞬时脉冲微分方程的周期解。构造了时变线性非瞬时脉冲系统的柯西矩阵，并推导了一些基本性质。用常变法和伴随矩阵求得充分必要条件$(\omega ,C)$- 齐次和非齐次系统的周期解。不动点定理用于证明存在性和唯一性$(\omega ,C)$给出了非线性系统的周期解和例子来说明理论结果。