In this paper we investigate sign-changing points of nontrivial real-valued
solutions of homogeneous Sturm-Liouville differential equations of the form
$-d(du/d\alpha)+ud\beta=0$, where $d\alpha$ is a positive Borel measure
supported everywhere on $(a,b)$ and $d\beta$ is a locally finite real Borel
measure on $(a,b)$. Since solutions for such equations are functions of locally
bounded variation, sign-changing points are the natural generalization of
zeros. We prove that sign-changing points for each nontrivial real-valued
solution are isolated in $(a,b)$. We also prove a Sturm-type separation theorem
for two nontrivial linearly independent solutions, and conclude the paper by
proving a Sturm-type comparison theorem for two differential equations with
distinct potentials.