Ф-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.本文借助中一函数理论,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Ф-有界变差解的情形,建立了此类不连续系统Ф-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.