The Properties of Eigenvalues and Eigenfunctions for Nonlocal Sturm–Liouville Problems

The present paper is concerned with the spectral theory of nonlocal Sturm–Liouville eigenvalue problems on a finite interval. The continuity, differentiability and comparison results of eigenvalues with respect to the nonlocal potentials are studied, and the oscillation properties of eigenfunctions...

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Bibliographic Details
Published in:Symmetry (Basel) Vol. 13; no. 5; p. 820
Main Authors: Liu, Zhiwen, Qi, Jiangang
Format: Journal Article
Language:English
Published: Basel MDPI AG 01.05.2021
Subjects:
Boundary conditions
Boundary value problems
Eigenvalues
Eigenvectors
Mathematical functions
Spectral theory
ISSN:2073-8994, 2073-8994
Online Access:Get full text
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Summary:The present paper is concerned with the spectral theory of nonlocal Sturm–Liouville eigenvalue problems on a finite interval. The continuity, differentiability and comparison results of eigenvalues with respect to the nonlocal potentials are studied, and the oscillation properties of eigenfunctions are investigated. The comparison result of eigenvalues and the oscillation properties of eigenfunctions indicate that the spectral properties of nonlocal problems are very different from those of classical Sturm–Liouville problems. Some examples are given to explain this essential difference.
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ISSN:2073-8994
2073-8994
DOI:10.3390/sym13050820