Sturm-Liouville problem with regular-singular point in the interval

Question

I am confronted with an eigenvalue problem on $\mathbb{R}$ whose differential equation has a regular-singular point at $x=0$. For that reason, I am interested to know if there are known results or general theory of Sturm-Liouville problems $$ (p(x)y(x)')'+q(x)y(x)=\lambda\sigma(x) y(x),\;\;x\in\mathbb{R}, \;\;\lim_{x\rightarrow\pm\infty}y=0, $$ where the ODE has a regular-singular point for some value of $x$. The classical Sturm-Liouville theory assumptions imply that there are no singular points on the interval of interest. Above, for the sake of example, I took the reals as the interval, together with vanishing boundary conditions. However, if results concerning finite intervals and/or other types of boundary conditions exist, I would be interested. I would also be interested if results would exist for non self-adjoint problems (i.e. not necessarily restricted to the Sturm-Liouville type).