Special cases of critical linear difference equations
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 se...
Elmentve itt :
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| Dokumentumtípus: | Folyóirat |
| Megjelent: |
2021
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| Sorozat: | Electronic journal of qualitative theory of differential equations
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| Kulcsszavak: | Differenciálegyenletek - lineáris |
| Tárgyszavak: | |
| doi: | 10.14232/ejqtde.2021.1.79 |
| Online Access: | http://acta.bibl.u-szeged.hu/75800 |
| Tartalmi kivonat: | 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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| Terjedelem/Fizikai jellemzők: | p. 1-17. |
| ISSN: | 1417-3875 |