Bounded Φ-Variation Solutions and H-K Integral

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.