Regularization of singular Sturm-Liouville equations - Mikhailets, V. A.; Goriunov, A. (Methods of Functional Analysis and Topology, 2010)
The paper deals with the singular Sturm-Liouville expressions l(y) = -(py’)’ + qy with the coefficients q = Q’, 1/p, Q/p, Q^2/p L_1, where the derivative of the function Q is understood in the sense of distributions. Due to a new regularization, the corresponding operators are correctly defined as quasi-differentials. 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 canonical form.