A Prüfer angle approach to singular Sturm–Liouville problems with Molčanov potentials

摘要

Singular Sturm–Liouville problems for -y″+qy=λy on (0,∞) are studied for potentials q which are bounded below and satisfy Molčanov's necessary and sufficient condition for discrete spectrum. A Prüfer angle approach is given for eigenvalue location and eigenfunction oscillation, paralleling that for the regular case. In particular, the eigenvalues are characterized by a “right-hand boundary condition” even though q is of limit point type.