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.$