Publication details

Special cases of critical linear difference equations

Investor logo


Year of publication 2021
Type Article in Periodical
Magazine / Source Electronic Journal of Qualitative Theory of Differential Equations
MU Faculty or unit

Faculty of Science

Keywords critical equations; linear difference equations; equations with interlacing indices
Description 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.
Related projects:

You are running an old browser version. We recommend updating your browser to its latest version.

More info