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Special cases of critical linear difference equations
- Source :
- Electronic Journal of Qualitative Theory of Differential Equations, Vol 2021, Iss 79, Pp 1-17 (2021)
- Publication Year :
- 2021
- Publisher :
- University of Szeged, 2021.
-
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.
Details
- Language :
- English
- ISSN :
- 14173875
- Volume :
- 2021
- Issue :
- 79
- Database :
- Directory of Open Access Journals
- Journal :
- Electronic Journal of Qualitative Theory of Differential Equations
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.b39e82dc1ade40ae9de26a3320163e6b
- Document Type :
- article
- Full Text :
- https://doi.org/10.14232/ejqtde.2021.1.79