Continuous Dependence and Differentiability of Solutions of Second-Order Impulsive Differential Equations on Initial Values and Impulsive Points

In this paper, we consider the continuous dependence and differentiability of solutions of second-order impulsive differential equations on initial values and impulsive points. By constructing a sequence of iterations, we show the existence of solutions with the perturbation of initial values and impulsive points and the continuous dependence of solution on initial values and impulsive points. Moreover, we also give a further result under some strong conditions. Based on these results, we present the result of differentiability of solutions on initial point and impulsive points. Finally, an example is provided to illustrate the practicability of our results.