Special cases of critical linear difference equations

Logo poskytovatele

Varování

Publikace nespadá pod Filozofickou fakultu, ale pod Přírodovědeckou fakultu. Oficiální stránka publikace je na webu muni.cz.
Autoři

JEKL Jan

Rok publikování 2021
Druh Článek v odborném periodiku
Časopis / Zdroj Electronic Journal of Qualitative Theory of Differential Equations
Fakulta / Pracoviště MU

Přírodovědecká fakulta

Citace
www https://doi.org/10.14232/ejqtde.2021.1.79
Doi http://dx.doi.org/10.14232/ejqtde.2021.1.79
Klíčová slova critical equations; linear difference equations; equations with interlacing indices
Popis 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.
Související projekty:

Používáte starou verzi internetového prohlížeče. Doporučujeme aktualizovat Váš prohlížeč na nejnovější verzi.