The HK-Sobolev space and applications to one-dimensional boundary value problems

Abstract

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.