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Axioms
Special Issues
Boundary-Value and Spectral Problems
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Boundary-Value and Spectral Problems

A special issue of Axioms (ISSN 2075-1680).

Deadline for manuscript submissions: closed (31 August 2022) | Viewed by 3837

Special Issue Editors

Prof. Dr. Vladimir Mikhailets

E-Mail Website
Guest Editor
Institute of Mathematics of National Academy of Sciences of Ukraine, 3 Tereshchenkivs’ka, 01004, Kyiv, Ukraine
Interests: functional analysis; operator theory; PDEs; ODEs; spectral theory; fourier analysis
Prof. Dr. Aleksandr Murach

E-Mail Website
Guest Editor
Institute of Mathematics of National Academy of Sciences of Ukraine, 3 Tereshchenkivs’ka, Kyiv 01004, Ukraine
Interests: functional analysis; operator theory; PDEs; ODEs; function spaces

Special Issue Information

Dear Colleagues,

We have launched a Special Issue of Axioms that will present current perspectives in the classical and modern development of the theory of boundary-value and spectral problems that address the interactions between differential equations, operator theory, and spectral theory. This issue will focus on the theory of boundary-value and spectral problems for ODEs, PDEs, and their applications. Differential equations have played a central role in mathematical modeling of a wide variety of phenomena in physics, biology, and other applied sciences. Boundary-value and spectral problems are a well-known but still quite active area of research. Their study is not only driven by theoretical interest but also the fact that these types of problems occur naturally when modeling real-world applications. We hope to provide a platform to bring together experts, as well as young researchers in the area to promote and share knowledge and to foster communications and applications. We invite research papers as well as review articles.

Prof. Dr. Vladimir Mikhailets
Prof. Dr. Aleksandr Murach
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

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-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Axioms is an international peer-reviewed open access monthly 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 2400 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 equation
  • Boundary condition
  • Periodic problem
  • Fredholm property
  • Index of operator
  • Schrӧdinger operator
  • Dirac operator
  • Hill equation
  • Quantum graph
  • Eigenvalues: asymptotics and inequalities
  • Spectrum
  • Inverse problem

Published Papers (2 papers)

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Research

23 pages, 427 KiB  
Article
Elliptic Problems with Additional Unknowns in Boundary Conditions and Generalized Sobolev Spaces
by Anna Anop, Iryna Chepurukhina and Aleksandr Murach
Axioms 2021, 10(4), 292; https://0-doi-org.brum.beds.ac.uk/10.3390/axioms10040292 - 03 Nov 2021
Cited by 4 | Viewed by 1030
Abstract
In generalized inner product Sobolev spaces we investigate elliptic differential problems with additional unknown functions or distributions in boundary conditions. These spaces are parametrized with a function OR-varying at infinity. This characterizes the regularity of distributions more finely than the number parameter used [...] Read more.
In generalized inner product Sobolev spaces we investigate elliptic differential problems with additional unknown functions or distributions in boundary conditions. These spaces are parametrized with a function OR-varying at infinity. This characterizes the regularity of distributions more finely than the number parameter used for the Sobolev spaces. We prove that these problems induce Fredholm bounded operators on appropriate pairs of the above spaces. Investigating generalized solutions to the problems, we prove theorems on their regularity and a priori estimates in these spaces. As an application, we find new sufficient conditions under which components of these solutions have continuous classical derivatives of given orders. We assume that the orders of boundary differential operators may be equal to or greater than the order of the relevant elliptic equation. Full article
(This article belongs to the Special Issue Boundary-Value and Spectral Problems)
7 pages, 235 KiB  
Article
Nonlocal Problem for a Third-Order Equation with Multiple Characteristics with General Boundary Conditions
by Abdukomil Risbekovich Khashimov and Dana Smetanová
Axioms 2021, 10(2), 110; https://0-doi-org.brum.beds.ac.uk/10.3390/axioms10020110 - 02 Jun 2021
Cited by 1 | Viewed by 1800
Abstract
The article considers third-order equations with multiple characteristics with general boundary value conditions and non-local initial data. A regular solution to the problem with known methods is constructed here. The uniqueness of the solution to the problem is proved by the method of [...] Read more.
The article considers third-order equations with multiple characteristics with general boundary value conditions and non-local initial data. A regular solution to the problem with known methods is constructed here. The uniqueness of the solution to the problem is proved by the method of energy integrals. This uses the theory of non-negative quadratic forms. The existence of a solution to the problem is proved by reducing the problem to Fredholm integral equations of the second kind. In this case, the method of Green’s function and potential is used. Full article
(This article belongs to the Special Issue Boundary-Value and Spectral Problems)
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