Special cases of critical linear difference equations

Electronic Journal of Qualitative Theory of Differential Equations

Jan Jekl¹ 

[1] Masaryk University, Brno, Czech Republic;

关键词: critical equations;    linear difference equations;    equations with interlacing indices;   

DOI  :  10.14232/ejqtde.2021.1.79

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown