In this paper, we consider the existence of multiple solutions for second-order equation with Stieltjes integral boundary condition using the three-critical-point theorem and variational method. Firstly, a novel space is established and proved to be Hilbert one. Secondly, based on the above work, we obtain the existence of multiple solutions for our problem. Finally, in order to illustrate the effectiveness of our problem better, the example is listed.

中文翻译：

---

具有Stieltjes积分边界条件的二阶问题的多重解的存在

本文利用三临界点定理和变分方法，考虑了具有Stieltjes积分边界条件的二阶方程的多重解的存在性。首先，建立了一个新颖的空间，并证明它是希尔伯特的空间。其次，基于上述工作，我们获得了针对我们问题的多种解决方案。最后，为了更好地说明我们的问题的有效性，列出了示例。