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Symmetry
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Symmetries in Differential Equations and Application—2nd Edition
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Symmetries in Differential Equations and Application—2nd Edition

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: 31 May 2025 | Viewed by 5111

Special Issue Editor

Prof. Dr. Cheon-Seoung Ryoo

E-Mail Website
Guest Editor
Department of Mathematics, Hannam University, Daejeon 34430, Republic of Korea
Interests: numerical verification method; scientific computing; differential equations; dynamical systems; quantum calculus; special functions
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The study of differential equations is a wide field in pure and applied mathematics. All of these fields relate to the properties of various types of differential equations.

Pure mathematics investigates the existence and uniqueness of solutions, while applied mathematics enforces a strict justification of how to approximate solutions.

Differential equations play a significant role in modeling virtually every physical, technical and biological process. These areas remain at the center of advanced mathematical research. Differential equations, such as those employed in order to solve real problems, are not necessarily directly solvable. Instead, solutions can be approximated using numerical methods. These methods are pivotal to studies in advanced mathematics, physics, and engineering, with many potential applications. Recently, differential equations have been closely related to several areas in mathematics, applied mathematics, physics, chemistry, biological sciences, and engineering, and have been employed to share recent knowledge and research in pure, as well as applied, mathematical sciences.

This Special Issue aims to publish major research papers and present the latest trends in pure and applied mathematical sciences, including the area of differential equations.

Prof. Dr. Cheon-Seoung Ryoo
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. Symmetry 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
  • symmetry
  • pseudo-differential operator
  • numerical analysis
  • approximation
  • a priori estimates
  • stability
  • asymptotic properties
  • numerical verification method
  • dynamical systems
  • quantum calculus
  • special functions

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

Published Papers (5 papers)

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Research

22 pages, 333 KiB  
Article
Asymptotic and Oscillatory Properties for Even-Order Nonlinear Neutral Differential Equations with Damping Term
by Belal Batiha, Nawa Alshammari, Faten Aldosari, Fahd Masood and Omar Bazighifan
Symmetry 2025, 17(1), 87; https://doi.org/10.3390/sym17010087 - 8 Jan 2025
Viewed by 373
Abstract
This research focuses on studying the asymptotic and oscillatory behavior of a special class of even-order nonlinear neutral differential equations, including damping terms. The research aims to achieve qualitative progress in understanding the relationship between the solutions of these equations and their associated [...] Read more.
This research focuses on studying the asymptotic and oscillatory behavior of a special class of even-order nonlinear neutral differential equations, including damping terms. The research aims to achieve qualitative progress in understanding the relationship between the solutions of these equations and their associated functions. Leveraging the symmetry between positive and negative solutions simplifies the derivation of criteria that ensure the oscillation of all solutions. Using precise techniques such as the Riccati method and comparison methods, innovative criteria are developed that guarantee the oscillation of all the solutions of the studied equations. The study provides new conditions and effective analytical tools that contribute to deepening the theoretical understanding and expanding the practical applications of these systems. Based on solid scientific foundations and previous studies, the research concludes with the presentation of examples that illustrate the practical impact of the results, highlighting the theoretical value of research in the field of neutral differential equations. Full article
(This article belongs to the Special Issue Symmetries in Differential Equations and Application—2nd Edition)
10 pages, 235 KiB  
Article
Ulam Stability of Second-Order Periodic Linear Differential Equations with Periodic Damping
by Jin Li, Xiaofang Xia, Chuanfang Zhang and Renlian Chen
Symmetry 2024, 16(11), 1459; https://doi.org/10.3390/sym16111459 - 3 Nov 2024
Viewed by 629
Abstract
We addressed the Ulam stability of second-order periodic linear differential equations with periodic damping. The necessary and sufficient conditions for the Ulam stability of second-order periodic linear differential equations were obtained by providing an Ulam stability theorem and an Ulam instability theorem. In [...] Read more.
We addressed the Ulam stability of second-order periodic linear differential equations with periodic damping. The necessary and sufficient conditions for the Ulam stability of second-order periodic linear differential equations were obtained by providing an Ulam stability theorem and an Ulam instability theorem. In particular, when the elastic coefficient remained constant at 0, a very general conclusion was obtained. These results expand on the conclusions in the relevant literature. In addition, for the situation of constant coefficients, the minimum Ulam constant is provided. Full article
(This article belongs to the Special Issue Symmetries in Differential Equations and Application—2nd Edition)
17 pages, 1071 KiB  
Article
Comparison Theorems for Oscillation of Higher-Order Neutral Delay Differential Equations
by Osama Moaaz, Hend Salah, Asma Al-Jaser, Mona Anis and Elmetwally M. Elabbasy
Symmetry 2024, 16(7), 903; https://doi.org/10.3390/sym16070903 - 15 Jul 2024
Viewed by 1348
Abstract
In this work, we study the oscillatory features of a class of neutral differential equations with multiple delays. We present novel oscillation conditions for this equation by using a comparison method. We create conditions that exclude the positive solution of the examined equation. [...] Read more.
In this work, we study the oscillatory features of a class of neutral differential equations with multiple delays. We present novel oscillation conditions for this equation by using a comparison method. We create conditions that exclude the positive solution of the examined equation. Using the feature of symmetry between non-oscillatory solutions (positive and negative), these conditions also exclude negative solutions without adding additional restrictions. In our study, we take into account the even and odd cases of the order of the equation. Furthermore, we study the asymptotic properties in three different cases of functional coefficients. Our results are a fundamental extension and generalization of previous relevant findings, and this fact has been demonstrated through comparisons. Full article
(This article belongs to the Special Issue Symmetries in Differential Equations and Application—2nd Edition)
►▼ Show Figures

Figure 1

Figure 1
<p>The lower bounds of <math display="inline"><semantics> <msub> <mi>q</mi> <mn>0</mn> </msub> </semantics></math>-values in conditions (<a href="#FD31-symmetry-16-00903" class="html-disp-formula">31</a>) and (<a href="#FD32-symmetry-16-00903" class="html-disp-formula">32</a>) when <math display="inline"><semantics> <mrow> <msub> <mi>p</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>.</p> Full article ">Figure 2
<p>The lower bounds of <math display="inline"><semantics> <msub> <mi>q</mi> <mn>0</mn> </msub> </semantics></math>-values in conditions (<a href="#FD31-symmetry-16-00903" class="html-disp-formula">31</a>) and (<a href="#FD32-symmetry-16-00903" class="html-disp-formula">32</a>) when <math display="inline"><semantics> <mrow> <mi>μ</mi> <mo>=</mo> <mn>0.2</mn> </mrow> </semantics></math>.</p> Full article ">Figure 3
<p>The lower bounds of <math display="inline"><semantics> <msub> <mi>q</mi> <mn>0</mn> </msub> </semantics></math>-values in conditions (<a href="#FD37-symmetry-16-00903" class="html-disp-formula">37</a>) and (<a href="#FD39-symmetry-16-00903" class="html-disp-formula">39</a>).</p> Full article ">Figure 4
<p>The lower bounds of <math display="inline"><semantics> <msub> <mi>q</mi> <mn>0</mn> </msub> </semantics></math>-values in conditions (<a href="#FD38-symmetry-16-00903" class="html-disp-formula">38</a>) and (<a href="#FD40-symmetry-16-00903" class="html-disp-formula">40</a>).</p> Full article ">Figure 5
<p>The lower bounds of <math display="inline"><semantics> <msub> <mi>q</mi> <mn>0</mn> </msub> </semantics></math>-values in conditions (<a href="#FD37-symmetry-16-00903" class="html-disp-formula">37</a>) and (<a href="#FD41-symmetry-16-00903" class="html-disp-formula">41</a>).</p> Full article ">
18 pages, 1324 KiB  
Article
Study of Quantum Difference Coupled Impulsive System with Respect to Another Function
by Nattapong Kamsrisuk, Chaiyod Kamthorncharoen, Sotiris K. Ntouyas and Jessada Tariboon
Symmetry 2024, 16(7), 897; https://doi.org/10.3390/sym16070897 - 14 Jul 2024
Viewed by 949
Abstract
In this paper, we study a quantum difference coupled impulsive system with respect to another function. Some quantum derivative and integral asymmetric graphs with respect to another function are shown to illustrate the behavior of parameters. Existence and uniqueness results are established via [...] Read more.
In this paper, we study a quantum difference coupled impulsive system with respect to another function. Some quantum derivative and integral asymmetric graphs with respect to another function are shown to illustrate the behavior of parameters. Existence and uniqueness results are established via Banach contraction mapping principle and Leray–Schauder alternative. Examples illustrating the obtained results are also included. Our results are new and significantly contribute to the literature to this new subject on quantum calculus on finite intervals with respect to another function. Full article
(This article belongs to the Special Issue Symmetries in Differential Equations and Application—2nd Edition)
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Figure 1

Figure 1
<p>Impact of quantum number <span class="html-italic">q</span> (<b>a</b>) and parameter <span class="html-italic">b</span> (<b>b</b>) on the quantum derivative of Example 1.</p> Full article ">Figure 2
<p>Impact of quantum number <span class="html-italic">q</span> (<b>a</b>) and parameter <span class="html-italic">b</span> (<b>b</b>) on the definite quantum integral of Example 2.</p> Full article ">Figure 3
<p>Visualization of solution function <span class="html-italic">s</span> for Example 5: (<b>a</b>) provides an overview of the entire domain, while (<b>b</b>–<b>d</b>) demonstrate the values of the function within each interval.</p> Full article ">Figure 4
<p>Visualization of solution function <span class="html-italic">r</span> for Example 5: (<b>a</b>) provides an overview of the entire domain, while (<b>b</b>–<b>d</b>) demonstrate the values of the function within each interval.</p> Full article ">
12 pages, 269 KiB  
Article
Non-Classical Symmetry Analysis of a Class of Nonlinear Lattice Equations
by Wenting Li, Yueting Chen and Kun Jiang
Symmetry 2023, 15(12), 2199; https://doi.org/10.3390/sym15122199 - 14 Dec 2023
Cited by 2 | Viewed by 1149
Abstract
In this paper, a non-classical symmetry method for obtaining the symmetries of differential–difference equations is proposed. The non-classical symmetry method introduces an additional constraint known as the invariant surface condition, which is applied after the infinitesimal transformation. By solving the governing equations that [...] Read more.
In this paper, a non-classical symmetry method for obtaining the symmetries of differential–difference equations is proposed. The non-classical symmetry method introduces an additional constraint known as the invariant surface condition, which is applied after the infinitesimal transformation. By solving the governing equations that satisfy this condition, we can obtain the corresponding reduced equation. This allows us to determine the non-classical symmetry of the differential–difference equation. This method avoids the complicated calculation involved in extending the infinitesimal generator and allows for a wider range of symmetry forms. As a result, it enables the derivation of a greater number of differential–difference equations. In this paper, two kinds of (2+1)-dimensional Toda-like lattice equations are taken as examples, and their corresponding symmetric and reduced equations are obtained using the non-classical symmetry method. Full article
(This article belongs to the Special Issue Symmetries in Differential Equations and Application—2nd Edition)
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Figure 1

Figure 1
<p>The plot of <math display="inline"><semantics> <mrow> <mi>u</mi> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> </semantics></math> (<a href="#FD72-symmetry-15-02199" class="html-disp-formula">72</a>).</p> Full article ">
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