ABSTRACT
The generalized Sturm-Liouville problems in this paper stem from the ideas of Shubin Christ and Stolz, based on introducing interface boundary conditions at a countable number of regular points on the real line.
This idea is generalized to the introduction of a countable number of regular or limit-circle singular points. These results are shown to link with the work of Everitt and Zettl concerned with operator theory generated by a countable number of symmetric differential expressions defined on intervals of the real line.
The results show that the Titchmarsh-Weyl dichotomy for integrable-square solutions can be extended and the corresponding 771-coefficient introduced. Certain associated self-adjoint operators can be characterised.
There are many applications of these results to one-dimensional Schrodinger equations thus extending earlier work of Gesztesy and Kirsch.
