Sturm-Liouville problems with an infinite number of interior singularities
نویسندگان
چکیده
The generalized Sturm-Liouville problems in this paper stem from the ideas of Christ Shubin and Stolz, based on introducing singularities 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 limitcircle 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 the the Titchmarsh-Weyl dichotomy for integrable-square solutions can be extended and the corresponding m-coefficient introduced. All associated self-adjoint operators can be characterised. There are many applications of these results to one-dimensional Schrödinger equations thus extending earlier work of Gesztesy and Kirsch.
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