On a class of singular Sturm–Liouville problems

A formally self-adjoint boundary value problem is under consideration. It corresponds to the formal differential equation $-(y'/r)'+q{}y=p{}f$, where $r$ and $p$ are generalized densities of two Borel measures which do not have common atoms and $q$ is a generalized function from some class related to the density $r.$ A self-adjoint operator generated by this boundary value problem is defined. The main term of the spectral asymptotics is established in the case when $r$ and $p$ are self-similar and $q=0.$