测度性奇异脉冲微分系统的某些基本理论的研究

Study on Some Fundamental Theories of Singular Measure Differential Systems with Impulse Effect

中文关键词  奇异测度系统  脉冲解  常数变易公式  等价性

英文关键词  singular measure systems  impulsive solution  variation of parameters formula  equivalence

中文摘要

      具有脉冲解的奇异测度微分系统的基本理论至今尚未建立，本文对这一问题进行了研究。首先建立了奇异测度微分系统与相应的奇异测度积分系统的等价性，然后借助于Drazin逆，在初始条件相容的情况下给出了线性奇异测度微分系统解的表达式，最后得到了一类非线性奇异测度微分系统的常数变易公式。

英文摘要

      Fundamental theory of the singular measure differential systems with impulsive solutions which have not been studied up to now is presented and taken into account. The equivalence between the singular measure differential systems and the corresponding singular measure integral equations is found. With the help of Drazin inverse, the solutions of the linear singular systems of differential equations with impulsive effects are obtained and the variation of parameters formula for a class of nonlinear singular measure differential systems is also established under the consistent initial conditions.