In this paper, we introduce the HK-Sobolev space and establish a fundamental theorem of calculus and an integration by parts formula, then we give sufficient conditions for the existence and uniqueness of a solution to a variational problem associated with a Sturm–Liouville type equation involving Henstock-Kurzweil integrable functions as source terms.

中文翻译：

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HK-Sobolev空间及其在一维边值问题中的应用

在本文中，我们介绍了HK-Sobolev空间，建立了微积分的基本定理和零件公式的积分，然后为与Sturm-Liouville型方程相关的变分问题的解的存在性和唯一性提供了充分的条件。涉及Henstock-Kurzweil可积函数作为源项。