Φ有界变差解与H-K积分

Bounded Φ-Variation Solutions and H-K Integral

Φ有界变差函数是有界变差函数的推广,而广义积分Henstock-Kurzweil是处理高度无限振荡函数的有效工具,运用Φ函数理论,定义了广义积分Henstock-Kurzweil意义下不连续系统的局部右行唯一性,将有界变差解推广到Φ有界变差解的情形,建立了Φ有界变差解的唯一性定理,对高度无限振荡问题的研究有一定的指导意义.

Bounded Φ-variation functions are generalization of bounded variation functions.The concept of Henstock-Kurzweil integral is an effective tool in dealing with infinite vibriation functions.By using Φ-function theory,the concept of locally right uniquenees in a discontinuous system is defined for generalized integrals in the sense of Henstock-Kurzweil.The bounded variation solution is generalized to bounded Φ variation solution and the uniquenees theorem for this solution is established.This result is of guidance in the research of infinite vibriation problem.