Principal solution in Weyl-Titchmarsh theory for second order Sturm-Liouville equation on time scales
| Authors | |
|---|---|
| Year of publication | 2017 |
| Type | Article in Periodical |
| Magazine / Source | Electronic Journal of Qualitative Theory of Differential Equations |
| MU Faculty or unit | |
| Citation | |
| Doi | http://dx.doi.org/10.14232/ejqtde.2017.1.2 |
| Field | General mathematics |
| Keywords | Sturmova-Liouvilleova rovnice; časová škála; Weylovo řešení; hlavní řešení; případ limitního bodu; případ limitního kruhu; kritéria |
| Attached files | |
| Description | A connection between the oscillation theory and the Weyl--Titchmarsh theory for the second order Sturm--Liouville equation on time scales is established by using the principal solution. In particular, it is shown that the Weyl solution coincides with the principal solution in the limit point case, and consequently the square integrability of the Weyl solution is obtained. Moreover, both limit point and oscillatory criteria are derived in the case of real-valued coefficients, while a~generalization of the invariance of the limit circle case is proven for complex-valued coefficients. Several of these results are new even in the discrete time case. Finally, some illustrative examples are provided. |
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