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      A new eigenvalue problem for the difference operator with nonlocal conditions

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          Abstract

          In the paper, the spectrum structure of one-dimensional differential operator with nonlocal conditions and of the difference operator, corresponding to it, has been exhaustively investigated. It has been proved that the eigenvalue problem of difference operator is not equivalent to that of matrix eigenvalue problem Au = λu, but it is equivalent to the generalized eigenvalue problem Au = λBu with a degenerate matrix B. Also, it has been proved that there are such critical values of nonlocal condition parameters under which the spectrum of both the differential and difference operator are continuous. It has been established that the number of eigenvalues of difference problem depends on the values of these parameters. The condition has been found under which the spectrum of a difference problem is an empty set. An elementary example, illustrating theoretical expression, is presented.

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          Most cited references 19

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          Arnoldi and Jacobi-Davidson methods for generalized eigenvalue problems $Ax=\lambda Bx$ with singular $B$

           Joost Rommes (2007)
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            Stepwise Stability for the Heat Equation with a Nonlocal Constraint

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              On the spectral stability in subspaces for difference schemes with nonlocal boundary conditions

               A. Gulin (2013)
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                Author and article information

                Journal
                Nonlinear Analysis: Modelling and Control
                Vilnius University Press
                1392-5113
                April 23 2019
                April 23 2019
                : 24
                : 3
                : 462-484
                Affiliations
                [1 ]Faculty of Mathematics and Informatics, Vilnius University
                [2 ]Vilnius Gediminas Technical University
                [3 ]Department of Applied Mathematics, Kaunas University of Technology
                [4 ]Institute of Data Science and Digital Technologies, Vilnius University
                Article
                10.15388/NA.2019.3.9
                © 2019

                All content is freely available without charge to users or their institutions. Users are allowed to read, download, copy, distribute, print, search, or link to the full texts of the articles in this journal without asking prior permission of the publisher or the author. Articles published in the journal are distributed under a http://creativecommons.org/licenses/by/4.0/.

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                Self URI (journal page): http://www.journals.vu.lt/

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