Bounded Variation Solutions For A Class Of Ordinary Differential Equations

In this paper,bounded variation solutions for the following retarded impulsive differential equation x(t)= f(t,xt),t?tk,k= 1,2,…,m,?x(tk)= Ik(x(tk)),t = tk,k = 1,2,…,m,(1)xt0+=? and the measure differential equation Dx = f(x,t)+ g(x,t)Du + p(t)Du(2)are studied by using the Kurzweil generalized differential equation.Drawing support from the Henstock-Kurzweil integral,the existence theorems of bounded variation solutions for this class of ordinary differential equations are established,which gen-eralizes some related results.This paper is organized as follows:we give some basic knowledge in first part;in second part we learn the existence theorem of bounded variation solution for retarded impulsive differential equation;the existence theorem of bounded variation solution for measure differential equation is established in part three.