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Differential Equations and Eigenvalue Problems with Application

A Special Issue of Mathematics (ISSN 2227-7390) belonging to the section "C1: Difference and Differential Equations".

Deadline for manuscript submissions: closed (15 September 2026) | Viewed by 589

Editor


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Guest Editor
Department of Mathematics, Shandong University, Weihai 264209, China
Interests: boundary value problems; Sturm–Liouville problem; spectral theory of differential operators; optimal recovery problems in spectral theory
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Differential equations and eigenvalue problems have been extensively and profoundly studied. Many differential and integral equations originate from physics, particularly eigenvalue problems that have clear physical meaning. They have long been an integral part of modern science and have numerous applications across the natural science and engineering.

This Special Issue focuses on recent theoretical and practical studies of differential equations and eigenvalue problems. Suitable topics include, but are not limited to, the following:

  • Differential and integral equations;
  • Boundary value problems;
  • Nonlocal problems;
  • Indefinite problems;
  • Differential operator spectrum theory;
  • Singular Sturm–Liouville differential operators;
  • Eigenvalue problems with application;
  • Asymptotic property of eigenvalues;
  • Continuous dependence of eigenvalues;
  • Gap and ratio of eigenvalues;
  • Inverse spectral problem;
  • Extremum problem;
  • Applications of eigenvalue problems.

Prof. Dr. Jiangang Qi
Guest Editor

Manuscript Submission Information

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Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-anonymized peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • differential and integral equations
  • boundary value problems
  • spectrum
  • differential operator spectrum theory

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Published Papers (1 paper)

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Research

21 pages, 334 KB  
Article
Globally Coupled Inverse Spectral Reconstruction for Discrete Sturm–Liouville Equations with Multiple Interior Discontinuities
by Bayram Bala
Mathematics 2026, 14(16), 2934; https://doi.org/10.3390/math14162934 - 13 Aug 2026
Viewed by 201
Abstract
This paper investigates inverse spectral problems for a class of discrete Sturm–Liouville operators with multiple transmission interfaces. The presence of several interfaces generates a coupled spectral structure in which the reconstruction of the operator coefficients is determined by a common generalized spectral function. [...] Read more.
This paper investigates inverse spectral problems for a class of discrete Sturm–Liouville operators with multiple transmission interfaces. The presence of several interfaces generates a coupled spectral structure in which the reconstruction of the operator coefficients is determined by a common generalized spectral function. A generalized spectral framework adapted to the multi-interface setting is introduced, and explicit reconstruction formulas for the associated tridiagonal coefficient matrix are derived. Using the corresponding Hankel moment determinants, it is shown that the interface coefficients are spectrally linked through the same moment sequence, producing a globally coupled reconstruction mechanism. In contrast to the single-interface case, the reconstruction cannot be decomposed into independent local procedures. A constructive recovery algorithm for the operator coefficients is obtained, and the role of the transmission parameters in the spectral representation is analyzed. An example illustrating the reconstruction process for multiple interfaces is also presented. Full article
(This article belongs to the Special Issue Differential Equations and Eigenvalue Problems with Application)
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