O.Dosly, R.Hilscher

A class of Sturm-Liouville difference equations: (non)oscillation constants and property BD

Abstract

In this paper we study oscillatory properties of the higher order Sturm-Liouville difference equation

(-1)n \Deltan (k\alpha \Deltan yk) = qkyk+n, \alpha\in R. (*)
In particular, we derive sufficient conditions for (non)oscillation of (*) and compute explicitly its (non)oscillation constants. The obtained results are used to derive necessary and sufficient conditions for discretenes and boundedness below of the spectrum of associated difference operators. We discuss also (non)oscillation of the Euler-type difference equation.



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Last change: February 1, 2001. (c) Roman Hilscher