Sturmian comparison theorems for three-term recurrence equations (Q1074032)

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.