Regular approximations of singular Sturm-Liouville problems with limit-circle endpoints
The authors investigate the general limit-circle Sturm-Liouville problem (SLP) with separated or coupled boundary conditions. A theory for continuous eigenvalue branches of a one-parameter family of ``induced realizations'' is established. Results are then extended from regular to singular SLPs for selfadjoint realization \(S\). Every eigenvalue of \(S\) is the limit of such a continuous eigenvalue branch. Cases of interest are when at least one endpoint is oscillatory or the leading coefficient function changes sign, leading to jump discontinuities in the continuous eigenvalue branch. Results could be used to construct algorithms for the numerical computation of eigenvalue of SLPs.
scientific article; zbMATH DE number 2119246
scientific article