On some class of singular Sturm-Liouville problems

Abstract

Sturm-Liouville spectral problem for equation $-(y^{\prime }/r{)}^{\prime }+qy=\lambda py$ with generalized functions $r\ge 0$, $q$ and $p$ is considered. It is shown that the problem may be reduced to analogous problem with $r\equiv 1$. The case of $q=0$ and self-similar $r$ and $p$ is considered as an example.

10 pages, in Russian, 1 figure, 1 table