In this work, we use techniques from Stieltjes calculus and fixed point index theory to show the existence and multiplicity of solution of a first order non-linear boundary value problem with linear boundary conditions that extend the periodic case. We also provide the Green’s function associated to the problem as well as an example of application.

中文翻译：

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基于拓扑方法的 Stieltjes 微分方程解的存在性和多重性

在这项工作中，我们使用 Stieltjes 微积分和不动点指数理论的技术来证明具有扩展周期性情况的线性边界条件的一阶非线性边值问题的解的存在性和多重性。我们还提供了与该问题相关的格林函数以及应用示例。