Publication details
Overview of Weyl-Titchmarsh theory for second order Sturm-Liouville equations on time scales
| Authors | |
|---|---|
| Year of publication | 2011 |
| Type | Article in Periodical |
| Magazine / Source | Int. J. Difference Equ. |
| MU Faculty or unit | |
| Citation | |
| Field | General mathematics |
| Keywords | Time scale; Weyl-Titchmarsh theory; Second order Sturm-Liouville dynamic equation; m(λ)-function; Weyl disk; Weyl circle; Limit point case; Limit circle case |
| Attached files | |
| Description | In this paper we present an overview of the basic Weyl-Titchmarsh theory for second order Sturm-Liouville equations on time scales. We construct m(lambda)-function, the Weyl solution, and Weyl disk. We justify the terminology ``disk'' by its geometric properties, show explicitly the coordinates of the center of the disk, and calculate its radius. We show that the dichotomy regarding the square-integrable solutions known in the continuous time and discrete theory works in the same way for general time scales. |
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