Spectral properties of differential operators with oscillating coefficients

We study the properties of singular Sturm-Liouville operators in Hilbert spaces. Although the literature on the topic is immense, there are a number of questions that have yet to be solved, for example, those pertaining to the behavior of solutions of the Sturm-Liouville equation with an irregular potential at infinity. This problem is topical not only for being of interest in itself but also because it naturally arises when dealing with questions related to the spectral properties of the Sturm-Liouville operator.