Investigation of a discrete Sturm–Liouville problem with two-point nonlocal boundary condition and natural approximation of a derivative in boundary condition

Abstract

The article investigates a discrete Sturm–Liouville problem with one natural boundary condition and another nonlocal two-point boundary condition. We analyze zeroes, poles and critical points of the characteristic function and how the properties of this function depend on parameters in nonlocal boundary condition. Properties of the Spectrum Curves are formulated and illustrated in figures.

Keywords

• discrete Sturm–Liouville problem
• natural condition
• nonlocal two-point condition
• spectrum curves