一类不连续系统Φ-有界变差解的唯一性(英文)  

Uniqueness of Bounded Φ-variation Solutions for a Class of Discontinuous System

作　　者：梁雪峰[1] 何万生[1] 李宝麟[2] 

机构地区：[1]天水师范学院数学与统计学院,天水741001 [2]西北师范大学数学与信息科学学院,兰州730070

出　　处：《工程数学学报》2012年第5期757-762,共6页Chinese Journal of Engineering Mathematics

基　　金：The National Natural Science Foundation of China(10571078);the Department ofEducation Research Fund of Gansu Province(0608-04)

摘　　要：Φ-有界变差函数是通常意义下有界变差函数的发展与推广,而Henstock-Kurzweil积分是处理高度无限振荡函数的有效工具.本文借助Φ-函数理论,给出了Henstock-Kurzweil积分意义下一类不连续系统的局部右行唯一性的定义,并且将该系统的有界变差解推广到了Φ-有界变差解的情形,建立了此类不连续系统Φ-有界变差解的Osgood型唯一性定理.这个结论是不连续系统有界变差解唯一性的本质推广,同时对研究高度无限振荡函数的有关问题奠定了一定的基础.BoundedФ-variation functions are development and generalization of bounded variation functions in the usual sense. The concept of Henstock-Kurzweil integral is an effective tool in dealing with highly infinite oscillation functions. In this paper, the concept of locally right uniquenees of a discontinuous system is defined for generalized integrals at the sense of Henstock-Kurzweil by usingФ-function theory. The bounded variation solution is generalized to bounded Ф-variation solution, and the Osgood-type uniqueness theorem for this solution of discontinuous system is established. This result is essential generalization of uniqueness for bounded variation solutions of the system, and the certain foundation is laid in the research of highly infinite oscillation functions.

关 键 词：Henstock-Kurzweil积分 不连续系统 Φ-有界变差解 

分 类 号：O175.12[理学—数学]