一类滞后脉冲微分方程有界变差解的唯一性

王佳,卢金芳

(西北师范大学数学与统计学院,甘肃 兰州 730070)

一类滞后脉冲微分方程有界变差解的唯一性

王佳,卢金芳

(西北师范大学数学与统计学院,甘肃 兰州 730070)

借助Henstock-Kurzweil积分,在建立了一类滞后脉冲微分方程有界变差解存在性定理的基础上,建立其解的唯一性定理并给出证明.这个结果将唯一性定理从Lebesgue积分意义下推广到Henstock-Kurzweil积分意义下.

滞后脉冲微分方程;局部有界变差;有界变差解;唯一性

1 引言

脉冲微分方程性质研究已有广泛的结果,在滞后脉冲微分方程的研究也有许多结果.关于滞后脉冲微分方程与广义常微分方程的关系最早由文献[1-2]提出.此后,文献[3]证明了它们的关系,同样的结果在文献[4]中进一步得到证明.

设G([a,b],Rn)是正则函数x:[a,b]→Rn所构成的空间,x(t)成为正则函数是指:x(t)的左右极限存在且有限,

显然,x在区间[t0,t0+σ]上是绝对连续的.

在本文中,对于滞后脉冲微分方程的条件比文献 [6]中更广泛.考虑的 f为 Henstock-Kurzweil可积且φ为正则函数.

本文结构分为四节:第二节中给出了Henstock-Kurzweil积分的定义以及控制收敛定理.第三节中回顾滞后脉冲微分方程并给出一些新的关于其解的相关结论.第四节中建立了滞后脉冲微分方程解的唯一性定理.

2 Henstock-Kurzweil积分与控制收敛定理

3 滞后脉冲微分方程

4 滞后脉冲微分方程有界变差解的唯一性

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Uniqueness of bounded variatonal solu tions for a class of im pu lsive retarded functional d iff erential equations

Wang Jia,Lu Jinfang
(College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,China)

In this paper,based on the existence theorem of bounded variation solution for im pu lsive retarded functional diff erential equations,using the Henstock-Kurzweil integral we estab lish the uniqueness theorem of bounded variation solution for these equations.This result generalizes theorem concerning uniqueness in Lebesgue integral setting to a Henstock-Kurzweil integral setting.

im pu lsive retarded diff erential equations,locally bounded variation solution, bounded variational solutions,uniqueness

O175.12

A

1008-5513(2012)06-0809-10

2012-09-05.

国家自然科学基金(11061031).

王佳(1987-),硕士生,研究方向：常微分方程拓扑动力系统.

2010 M SC:35A 02