Characteristic functions for sturm—liouville problems with nonlocal boundary conditions

Abstract

This paper presents some new results on a spectrum in a complex plane for the second order stationary differential equation with one Bitsadze‐Samarskii type nonlocal boundary condition. In this paper, we survey the characteristic function method for investigation of the spectrum of this problem. Some new results on characteristic functions are proved. Many results of this investigation are presented as graphs of characteristic functions. A definition of constant eigenvalues and the characteristic function is introduced for the Sturm‐Liouville problem with general nonlocal boundary conditions.

Key words:

• Sturm‐Liouville problem
• nonlocal boundary conditions

Notes

This work was partially supported by the Lithuanian State Science and Studies Foundation within the project on T‐73/09 “Methods for Solving Parabolic and Navier—Stokes Differential Equations with Nonlocal Conditions”.