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Journals
Axioms
Special Issues
Recent Advances in Differential Equations and Related Topics
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Recent Advances in Differential Equations and Related Topics

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: 28 February 2026 | Viewed by 755

Special Issue Editors

Dr. Loredana Florentina Iambor

E-Mail Website
Guest Editor
Department of Mathematics and Computer Science, University of Oradea, Univeritatii nr. 1, 410087 Oradea, Romania
Interests: applied mathematics; differential equations; fixed point theory; approximation theory
Prof. Dr. Ram N. Mohapatra

E-Mail Website
Guest Editor
Department of Mathematics, University of Central Florida, Orlando, FL 10587, USA
Interests: functional analysis; differential equations; fixed point theory; variational inequalities; approximation theory

Special Issue Information

Dear Colleagues,

The study of differential equations forms the subject of a very important chapter of mathematics, both due to the countless applications in various fields, such as physics, chemistry, biology, engineering, economics, medicine, etc., as well as due to the mathematical apparatus necessary to solve them.

From the classical formulation of these equations, through ordinary derivatives, different classes of differential equations were obtained such as: delay, fractional, functional or integro-differential equations.

This Special Issue aims to bring new results of mathematicians together with those of physicists, biologists, engineers and other scientists, for whom differential equations are valuable research tools.

This Special Issue is dedicated, but not limited, to the following topics of interest:

  • Ordinary and partial differential equations;
  • Differential–difference equations;
  • Approximation, stability, boundedness, periodicity, and asymptotic properties;
  • Delay differential equations;
  • Fractional differential equations;
  • Integro-differential equations;
  • Functional equations;
  • Numerical methods for differential equations.

Dr. Loredana Florentina Iambor
Prof. Dr. Ram N. Mohapatra
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

  • ordinary and partial differential equations
  • differential–difference equations
  • approximation, stability, boundedness, periodicity, and asymptotic properties
  • delay differential equations
  • fractional differential equations
  • integro-differential equations
  • functional equations
  • numerical methods for differential equations

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Further information on MDPI's Special Issue policies can be found here.

Published Papers (2 papers)

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13 pages, 276 KiB  
Article
Ground State for a Schrödinger–Born–Infeld System via an Approximating Procedure
by Gaetano Siciliano
Axioms 2025, 14(7), 481; https://doi.org/10.3390/axioms14070481 - 20 Jun 2025
Viewed by 149
Abstract
In this paper we discuss some results on the existence of solutions for an elliptic system appearing in physical sciences. In particular the system appears when we look at standing wave solutions in the electrostatic situation for the Schrödinger equation coupled, with the [...] Read more.
In this paper we discuss some results on the existence of solutions for an elliptic system appearing in physical sciences. In particular the system appears when we look at standing wave solutions in the electrostatic situation for the Schrödinger equation coupled, with the minimal coupling rule, with the electromagnetic equations of Born–Infeld theory. Many difficulties appear, especially due to the fact we are in an unbounded domain (the whole space R3) and to the intrinsic nonlinear nature of the equations. We are able to prove the existence of a minimal energy solution by showing an approximating procedure that can be adapted depending on the value of the parameter p, which is in the nonlinearity. Full article
(This article belongs to the Special Issue Recent Advances in Differential Equations and Related Topics)
25 pages, 1055 KiB  
Article
A Layer-Adapted Numerical Method for Singularly Perturbed Partial Functional-Differential Equations
by Ahmed A. Al Ghafli, Fasika Wondimu Gelu and Hassan J. Al Salman
Axioms 2025, 14(5), 362; https://doi.org/10.3390/axioms14050362 - 12 May 2025
Viewed by 266
Abstract
This article describes an effective computing method for singularly perturbed parabolic problems with small negative shifts in convection and reaction terms. To handle the small negative shifts, the Taylor series expansion is used. The asymptotically equivalent singularly perturbed parabolic convection–diffusion–reaction problem is then [...] Read more.
This article describes an effective computing method for singularly perturbed parabolic problems with small negative shifts in convection and reaction terms. To handle the small negative shifts, the Taylor series expansion is used. The asymptotically equivalent singularly perturbed parabolic convection–diffusion–reaction problem is then discretized with the Crank–Nicolson method on a uniform mesh for the time derivative and a hybrid method on Shishkin-type meshes for the space derivative. The method’s stability and parameter-uniform convergence are established. To substantiate the theoretical findings, the numerical results are presented in tables and graphs are plotted. The present results improve the existing methods in the literature. Due to the effect of the small negative shifts in Examples 1 and 2, the numerical results using Shishkin and Bakhvalov–Shishkin meshes are almost the same. Since there are no small shifts in Examples 3 and 4, the numerical results using the Bakhvalov–Shishkin mesh are more efficient than using the Shishkin mesh. We conclude that the present method using the Bakhvalov–Shishkin mesh performs well for singularly perturbed problems without small negative shifts. Full article
(This article belongs to the Special Issue Recent Advances in Differential Equations and Related Topics)
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