Special cases of critical linear difference equations
| Authors | |
|---|---|
| Year of publication | 2021 |
| Type | Article in Periodical |
| Magazine / Source | Electronic Journal of Qualitative Theory of Differential Equations |
| MU Faculty or unit | |
| Citation | |
| Web | https://doi.org/10.14232/ejqtde.2021.1.79 |
| Doi | http://dx.doi.org/10.14232/ejqtde.2021.1.79 |
| Keywords | critical equations; linear difference equations; equations with interlacing indices |
| Description | In this paper, we investigate even-order linear difference equations and their criticality. However, we restrict our attention only to several special cases of the general Sturm–Liouville equation. We wish to investigate on such cases a possible converse of a known theorem. This theorem holds for second-order equations as an equivalence; however, only one implication is known for even-order equations. First, we show the converse in a sense for one term equations. Later, we show an upper bound on criticality for equations with nonnegative coefficients as well. Finally, we extend the criticality of the second-order linear self-adjoint equation for the class of equations with interlacing indices. In this way, we can obtain concrete examples aiding us with our investigation. |
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