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

摘要：

Bounded Φ-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 using Φ-function theory. The bounded variation solution is generalized to bounded Φ-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 integral、discontinuous system、bounded Φ-variation solution

分类号：O175.12(数学分析)

在线出版日期：2012-11-06（万方平台首次上网日期，不代表论文的发表时间）

页数：共6页

页码：757-762