Jekl Jan: Special cases of critical linear difference equations. (2021)
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Abstract
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.
| Item Type: | Journal |
|---|---|
| Publication full: | Electronic journal of qualitative theory of differential equations |
| Date: | 2021 |
| Number: | 79 |
| ISSN: | 1417-3875 |
| Pages note: | p. 1-17. |
| Language: | English |
| Place of Publication: | Szeged |
| DOI: | 10.14232/ejqtde.2021.1.79 |
| Uncontrolled Keywords: | Differenciálegyenletek - lineáris |
| Additional Information: | Bibliogr.: p. 14-17. ; összefoglalás angol nyelven |
| Subjects: | 01. Natural sciences 01. Natural sciences > 01.01. Mathematics |
| Date Deposited: | 2022. May. 23. 11:14 |
| Last Modified: | 2022. May. 23. 11:18 |
| URI: | http://acta.bibl.u-szeged.hu/id/eprint/75800 |
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