The Bounded φ-Variation Solutions Of A Kind Of Discontinuous System

In this paper,we discuss the bounded Φ-variation solutions of the Caratheodory system by combining the theories of function of bounded Φ-variation and the Caratheodory system.On the whole,we do as follows:Firstly,we list some conceptions and lemmas to be applied in this paper.Secondly,we discuss the existence theorem for bounded Φ-variation solutions of the Caratheodory system.Thirdly,we discuss the uniqueness theorem for bounded Φ-variation solutions of the Caratheodory system.Fourly,we present the continuous dependence theorem on a parameter of bounded Φ-variation solutions .Finally,we discuss the properties for sets of bounded Φ-variation solutions of the Caratheodory system .