In this paper, we consider the existence of positive solutions for one dimensional Minkowski curvature problem with either singular weight function or singular nonlinear term. By virtue of fixed point arguments and perturbation technique, we establish the new existence results of positive solutions under different assumptions on the nonlinear term. Moreover, some examples are also given as applications.

中文翻译：

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一维奇异性闵可夫斯基曲率问题正解的存在性

在本文中，我们考虑具有奇异权函数或奇异非线性项的一维闵可夫斯基曲率问题的正解的存在性。借助不动点论证和摄动技术，我们建立了非线性项不同假设下正解的新的存在性结果。此外，还给出了一些示例作为应用。