一類滯后脈沖微分方程有界變差解的唯一性

王佳,盧金芳

(西北師范大學數學與統計學院,甘肅 蘭州 730070)

一類滯后脈沖微分方程有界變差解的唯一性

王佳,盧金芳

(西北師范大學數學與統計學院,甘肅 蘭州 730070)

借助Henstock-Kurzweil積分,在建立了一類滯后脈沖微分方程有界變差解存在性定理的基礎上,建立其解的唯一性定理并給出證明.這個結果將唯一性定理從Lebesgue積分意義下推廣到Henstock-Kurzweil積分意義下.

滯后脈沖微分方程;局部有界變差;有界變差解;唯一性

1 引言

脈沖微分方程性質研究已有廣泛的結果,在滯后脈沖微分方程的研究也有許多結果.關于滯后脈沖微分方程與廣義常微分方程的關系最早由文獻[1-2]提出.此后,文獻[3]證明了它們的關系,同樣的結果在文獻[4]中進一步得到證明.

設G([a,b],Rn)是正則函數x:[a,b]→Rn所構成的空間,x(t)成為正則函數是指:x(t)的左右極限存在且有限,

顯然,x在區間[t0,t0+σ]上是絕對連續的.

在本文中,對于滯后脈沖微分方程的條件比文獻 [6]中更廣泛.考慮的 f為 Henstock-Kurzweil可積且φ為正則函數.

本文結構分為四節:第二節中給出了Henstock-Kurzweil積分的定義以及控制收斂定理.第三節中回顧滯后脈沖微分方程并給出一些新的關于其解的相關結論.第四節中建立了滯后脈沖微分方程解的唯一性定理.

2 Henstock-Kurzweil積分與控制收斂定理

3 滯后脈沖微分方程

4 滯后脈沖微分方程有界變差解的唯一性

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[5]Fedrson M,Schwabik S.Generalized ODEs approach to im pulsive retarded diff erential equations[J].Diff erential and Integral Equations,2006,19:1201-1234.

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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.

國家自然科學基金(11061031).

王佳(1987-),碩士生,研究方向：常微分方程拓撲動力系統.

2010 M SC:35A 02