Regularization of singular Sturm-Liouville equations

Paper deals with the singular Sturm-Liouville expressions $$l(y)=-(p{y}^{\mathrm{\prime }}{)}^{\mathrm{\prime }}+qy$$ on a finite interval with coefficients $$q=Q^{\mathrm{\prime }},1\mathrm{/}p,Q\mathrm{/}p,Q^2\mathrm{/}p\in L_1,$$ where derivative of the function $Q$ is understood in the sense of distributions. Due to a new regularization corresponding operators are correctly defined as quasi-differential. Their resolvent approximation is investigated and all self-adjoint and maximal dissipative extensions and generalized resolvents are described in terms of homogeneous boundary conditions of the canonic form. Some results are new for the case $p(t)\equiv 1$ as well.