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In this paper we investigate sign-changing points of nontrivial real-valuedsolutions of homogeneous Sturm-Liouville differential equations of the form$-d(du/d\alpha)+ud\beta=0$, where $d\alpha$ is a positive Borel measuresupported everywhere on $(a,b)$ and $d\beta$ is a locally finite real Borelmeasure on $(a,b)$. Since solutions for such equations are functions of locallybounded variation, sign-changing points are the natural generalization ofzeros. We prove that sign-changing points for each nontrivial real-valuedsolution are isolated in $(a,b)$. We also prove a Sturm-type separation theoremfor two nontrivial linearly independent solutions, and conclude the paper byproving a Sturm-type comparison theorem for two differential equations withdistinct potentials.

Sign-Changing Points of Solutions of Homogeneous Sturm-Liouville Equations with Measure-Valued Coefficients