In this article, we consider the existence of upper and lower solutions to a second-order random impulsive differential equation. We first study the solution form of the corresponding linear impulsive system of the second-order random impulsive differential equation. Based on the form of the solution, we define the resolvent operator. Then, we prove that the fixed point of this operator is the solution to the equation. Finally, we construct the sum of two monotonic iterative sequences and prove that they are convergent. Thus, we conclude that the system has upper and lower solutions.

中文翻译：

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具有边值问题的二阶随机脉冲微分方程上下解的存在性

在本文中，我们考虑了二阶随机脉冲微分方程的上下解的存在性。我们首先研究二阶随机脉冲微分方程的相应线性脉冲系统的解形式。根据解决方案的形式，我们定义可分辨运算符。然后，证明该算子的不动点是方程的解。最后，我们构造了两个单调迭代序列的总和，并证明它们是收敛的。因此，我们得出结论，该系统具有上下解决方案。