Study of first order Discontinuous ordinary Differential Equations

In this present paper, the existence and uniqueness theorems for the first order discontinuous differential equations have been obtained through Ascoli-Arzela theorem and Banach fixed point principle under the generalized measurability and Lipschitzicity conditions. An existence theorem and the maximum interval for the existence of the solution are also obtained without using the generalized Lipchitz condition and is a nonlinear alternative of Granas et. al.