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

In this paper, we study oscillatory properties of the higher-order Sturm-Liouville difference equation (−1)nΔn(k(α)Δnyk)=qkyk+n, α ε 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 discreteness and boundedness below the spectrum of associated difference operators. We discuss also (non)oscillation of the Euler-type difference equation.