Regularization of singular Sturm-Liouville equations

Abstract

Paper deals with the singular Sturm-Liouville expressions $$l(y)=-(p{y}^{\prime }{)}^{\prime }+qy$$ on a finite interval with coefficients $$q=Q^{\prime },1/p,Q/p,Q^2/p\in L_1,$$ 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.

12 pages

Cited by in corpus (1)

• Weyl-Titchmarsh Theory for Sturm-Liouville Operators with Distributional Potentials