Discontinuous Systems and the Henstock]Kurzweil Integral*

By using the Henstock]Kurzweil integral and the inequalities of this integral, the existence and uniqueness theorems for the solution of the discontinuous Caratheodory system are established. The results are generalizations of earlier investigations wJ. He and Po Chen, Ad¨. in Math. 16 1987., 17]32 in Chinese.; A. F. Filippov, Math. USSR-Sb. 51 1960. in Russian.; O. Hajek, J. Differential Equations 32 1979., 149]185x of this discontinuous system