Open AccessOn the equivalence of discrete Sturm–Liouville problem with nonlocal boundary conditions to the algebraic eigenvalue problem
Author(s) -
Jurij Novickij,
Artūras Štikonas
Publication year - 2015
Publication title -
lietuvos matematikos rinkinys
Language(s) - English
Resource type - Journals
eISSN - 2335-898X
pISSN - 0132-2818
DOI - 10.15388/lmr.a.2015.12
Subject(s) - eigenvalues and eigenvectors , sturm–liouville theory , mathematics , equivalence (formal languages) , algebraic number , boundary value problem , mathematical analysis , order (exchange) , algebraic equation , pure mathematics , physics , nonlinear system , finance , quantum mechanics , economics
As a result of technological progress during the last couple decades, there has been an interest investigating problems with rather complicated nonclassical conditions modeling natural, physical, chemical and other processes [4]. In connection with this fact it is natural to investigate whether the problem is well-posed. To understand the behaviour of real processes it is natural to investigate solvability condition on the stationary problems. The solvability results for various type differential problems with nonlocal conditions can be found in [1]. In the present paper, we investigate the solvability of the discrete Sturm–Liouville problem with two nonlocal boundary conditions (NBC) of the general form. We investigate the condition when the discrete Sturm–Liouville problem can be transformed to an algebraic eigenvalue problem. We also provide the examples of the solvability conditions for the most popular nonlocal boundary conditions.