Investigation of spectrum curves for a Sturm-Liouville problem with two-point nonlocal boundary conditions

Abstract

The article investigates the Sturm–Liouville problem with one classical 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 for various values of parameter ξ.

Keywords

• Sturm–Liouville problem
• nonlocal two-point condition
• eigenvalues
• critical points
• spectrum curves