Special cases of critical linear difference equations

Jekl Jan: Special cases of critical linear difference equations. (2021)

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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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