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Mathematics
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Contemporary Generalizations of Differential Equations and Related Enhancements in Analysis
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Contemporary Generalizations of Differential Equations and Related Enhancements in Analysis

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Difference and Differential Equations".

Deadline for manuscript submissions: closed (1 February 2024) | Viewed by 1897

Special Issue Editor

Dr. Andrey Borisovich Muravnik

E-Mail Website
Guest Editor
Nikol’skii Mathematical Institute, Peoples' Friendship University of Russia, 117198 Moscow, Russia
Interests: partial differential equations and related areas of analysis

Special Issue Information

Dear Colleagues,

Differential equations have been one of the most important and influential fields of mathematics for centuries, with wide-ranging applications in physics, engineering, finance, and many other fields. The study of differential equations has led to many important discoveries, and researchers have developed a variety of techniques to solve them. In recent years, the study of differential equations has expanded to include various generalizations.

This Special Issue aims to include research papers and surveys covering a wide range of topics in pure and applied mathematics. High-quality papers on the following topics are welcome: functional-differential equations, fractional-order differential equations, degenerate and singular differential equations, and nonlinear differential equations. Related areas of analysis within the framework of the Special Issue include: spectral theory, weight functions spaces, special functions, integral transformations, nonlocal aspects of functional analysis, nonlinear analysis, asymptotical analysis, and applications of all the above-mentioned theoretical directions.

Dr. Andrey Borisovich Muravnik
Guest Editor

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. 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

  • estimates of solutions
  • nonlocal properties
  • qualitative behavior
  • spectral problems
  • boundary-value problems
  • nonlocal problems
  • Fourier analysis
  • integrals and derivatives of fractional orders
  • nonclassical integral transformations

Published Papers (3 papers)

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Research

33 pages, 500 KiB  
Article
Resolvent Convergence for Differential–Difference Operators with Small Variable Translations
by Denis Ivanovich Borisov and Dmitry Mikhailovich Polyakov
Mathematics 2023, 11(20), 4260; https://doi.org/10.3390/math11204260 - 12 Oct 2023
Viewed by 497
Abstract
We consider general higher-order matrix elliptic differential–difference operators in arbitrary domains with small variable translations in lower-order terms. The operators are introduced by means of general higher-order quadratic forms on arbitrary domains. Each lower-order term depends on its own translation and all translations [...] Read more.
We consider general higher-order matrix elliptic differential–difference operators in arbitrary domains with small variable translations in lower-order terms. The operators are introduced by means of general higher-order quadratic forms on arbitrary domains. Each lower-order term depends on its own translation and all translations are governed by a small multi-dimensional parameter. The operators are considered either on the entire space or an arbitrary multi-dimensional domain with a regular boundary. The boundary conditions are also arbitrary and general and involve small variable translations. Our main results state that the considered operators converge in the norm resolvent sense to ones with zero translations in the best possible operator norm. Estimates for the convergence rates are established as well. We also prove the convergence of the spectra and pseudospectra. Full article
(This article belongs to the Special Issue Contemporary Generalizations of Differential Equations and Related Enhancements in Analysis)
22 pages, 415 KiB  
Article
Local Solvability and Stability of an Inverse Spectral Problem for Higher-Order Differential Operators
by Natalia P. Bondarenko
Mathematics 2023, 11(18), 3818; https://doi.org/10.3390/math11183818 - 5 Sep 2023
Cited by 2 | Viewed by 567
Abstract
In this paper, we, for the first time, prove the local solvability and stability of an inverse spectral problem for higher-order (n>3) differential operators with distribution coefficients. The inverse problem consists of the recovery of differential equation coefficients from [...] Read more.
In this paper, we, for the first time, prove the local solvability and stability of an inverse spectral problem for higher-order (n>3) differential operators with distribution coefficients. The inverse problem consists of the recovery of differential equation coefficients from (n−1) spectra and the corresponding weight numbers. The proof method is constructive. It is based on the reduction of the nonlinear inverse problem to a linear equation in the Banach space of bounded infinite sequences. We prove that, under a small perturbation of the spectral data, the main equation remains uniquely solvable. Furthermore, we estimate the differences of the coefficients in the corresponding functional spaces. Full article
(This article belongs to the Special Issue Contemporary Generalizations of Differential Equations and Related Enhancements in Analysis)
17 pages, 370 KiB  
Article
(F, G, C)-Resolvent Operator Families and Applications
by Vladimir E. Fedorov and Marko Kostić
Mathematics 2023, 11(16), 3505; https://doi.org/10.3390/math11163505 - 14 Aug 2023
Viewed by 571
Abstract
In this paper, we introduce and investigate several new classes of (F,G,C)-regularized resolvent operator families subgenerated by multivalued linear operators in locally convex spaces. The known classes of (a,k)-regularized C-resolvent [...] Read more.
In this paper, we introduce and investigate several new classes of (F,G,C)-regularized resolvent operator families subgenerated by multivalued linear operators in locally convex spaces. The known classes of (a,k)-regularized C-resolvent operator-type families are special cases of the classes introduced in this paper. We provide certain applications of (F,G,C)-regularized resolvent operator families and (a,k)-regularized C-resolvent families to abstract fractional differential–difference inclusions and abstract Volterra integro-difference inclusions. Full article
(This article belongs to the Special Issue Contemporary Generalizations of Differential Equations and Related Enhancements in Analysis)
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