一定条件下,测度微分方程与广义常微分方程等价,从而,广义常微分方程的一些理论可应用于测度微分方程,相关文献已讨论了广义常微分方程的解相对于初始条件的可微性,而且这一理论可应用于其他类型的方程.为此本文中,利用广义常微分方程的解相对于初始条件的可微性得到测度微分方程的解相对于初始条件的可微性定理.
Under some conditions, we have known that measure differential equations are equivalent to the generalized ordinary differential equations, so we can apply some theories of generalized differential equations in the measure differential equations. And there are many sources describe the solutions of generalized ordinary differential equations are differentiable with respect to initial conditions, this result applied and extends several existing theorems for other equations. Therefore, the differentiability of solutions with respect to initial conditions for measure differential equations are established in this paper by using the differentiability of solutions with respect to initial conditions for generalized ordinary differential equations.