Generalized solutions of differential equations with discontinuous terms in Banach spaces

The results of existence and uniqueness of solutions for differential equation initial value problem u′=f(t,u),u(0)=x 0 in ordered Banach spaces are obtained by using the monotone iterative method with upper and lower solutions.Where f:I×EE ,which does not require to be continuous,only satisfies the condition of mapping continuous functions into strongly measurabe functions.