Open AccessCHARACTERISTIC FUNCTIONS FOR STURM—LIOUVILLE PROBLEMS WITH NONLOCAL BOUNDARY CONDITIONS
Author(s) -
Artūras Štikonas,
Olga Štikonienė
Publication year - 2009
Publication title -
mathematical modelling and analysis/mathematical modeling and analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.491
H-Index - 25
eISSN - 1648-3510
pISSN - 1392-6292
DOI - 10.3846/1392-6292.2009.14.229-246
Subject(s) - mathematics , eigenvalues and eigenvectors , mathematical analysis , sturm–liouville theory , spectrum (functional analysis) , boundary value problem , boundary (topology) , function (biology) , type (biology) , plane (geometry) , differential equation , complex plane , physics , geometry , ecology , quantum mechanics , evolutionary biology , biology
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.