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Sturmian comparison theorems for three-term recurrence equations. (English) Zbl 0589.39002
The author considers a discrete analogue of an ordinary, regular, self- adjoint second-order differential equation. For these homogeneous difference equations (or recurrences) with homogeneous discrete boundary conditions of Sturm-Liouville type, several comparison theorems concerning the existence and inclusion of nodes of the corresponding non- trivial solutions are derived. The concept of nodes used here is based on the zeros of a linear spline, interpolating the components of a vector.
Reviewer: G.Meinardus

MSC:
39A10Additive difference equations
39A12Discrete version of topics in analysis