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Mathematics
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Advances in Nonlinear Differential Equations with Applications
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Advances in Nonlinear Differential Equations with Applications

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "C1: Difference and Differential Equations".

Deadline for manuscript submissions: 31 January 2026 | Viewed by 1320

Special Issue Editors

Prof. Dr. Wei-Chuan Wang

E-Mail Website
Guest Editor
Center for General Education, National Quemoy University, Kinmen, Taiwan
Interests: differential equation; analysis
Prof. Dr. Tsu-Ming Yeh

E-Mail Website
Guest Editor
Department of Industrial Engineering and Management, National Quemoy University, Kinmen County 892, Taiwan
Interests: operations management; decision analysis; human resources management
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The aim of this Special Issue is to present innovative research and advancements in the field of nonlinear differential equations and management, encompassing both theoretical developments and practical applications.

This Special Issue welcomes the submission of high-quality articles that present original research supported by illustrative applications, as well as survey articles of exceptional merit that offer advanced insights into the field. The scope of this Special Issue includes, but is not limited to, the following topics:

  • Analytical and numerical methods for solving nonlinear differential equations;
  • Stability analysis and bifurcation theory;
  • Nonlinear dynamic systems and chaos theory;
  • Fractional differential equations and their applications.

We encourage submissions that highlight the interplay between theoretical foundations and real-world applications, fostering a deeper understanding of nonlinear phenomena across various domains.

Prof. Dr. Wei-Chuan Wang
Prof. Dr. Tsu-Ming Yeh
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 250 words) can be sent to the Editorial Office for assessment.

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

  • nonlinear differential equations
  • the existence result
  • the classification of solutions
  • applications in management

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

Published Papers (4 papers)

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Research

9 pages, 241 KB  
Article
Critical Poles and Third-Order Nonlinear Differential Equations
by Victor Orlov
Mathematics 2025, 13(24), 3989; https://doi.org/10.3390/math13243989 - 15 Dec 2025
Abstract
The paper deals with the results of a study of a third-order nonlinear differential equation with moving singular points and critical poles. So far, this type of equation cannot be solved in quadratures. The development of the author’s approach in proving the theorem [...] Read more.
The paper deals with the results of a study of a third-order nonlinear differential equation with moving singular points and critical poles. So far, this type of equation cannot be solved in quadratures. The development of the author’s approach in proving the theorem of the existence of moving singular points and solutions in the vicinity of a critical pole, based on a modified Cauchy majorant method, is given. An analytical approximate solution in the vicinity of a moving singular point is obtained, and an expression for the a priori error estimate is presented. A numerical experiment confirming the obtained theoretical results is provided. Full article
(This article belongs to the Special Issue Advances in Nonlinear Differential Equations with Applications)
10 pages, 764 KB  
Article
Exact Solution and Bifurcation Curve for the Minkowski-Curvature Equation with Nonlinearity up+uq, p > 1
by Yan-Hsiou Cheng and Kuo-Chih Hung
Mathematics 2025, 13(22), 3680; https://doi.org/10.3390/math13223680 - 17 Nov 2025
Viewed by 208
Abstract
We study the bifurcation curve and exact multiplicity of positive solutions in the space C2(−L,L)∩C[−L,L] for the Minkowski-curvature equation: [...] Read more.
We study the bifurcation curve and exact multiplicity of positive solutions in the space C2(−L,L)∩C[−L,L] for the Minkowski-curvature equation: −u′(x)1−u′(x)2′=λup+uq,−L<x<L;u(−L)=u(L)=0, where λ,L>0 and p>1. If 1<p<q≤2p+3p2−3, we prove that the bifurcation curve is ⊂-shaped. Full article
(This article belongs to the Special Issue Advances in Nonlinear Differential Equations with Applications)
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12 pages, 274 KB  
Article
Cauchy Problems for Semilinear Parabolic Equations in Grand Herz Spaces
by Suixin He and Ronghui Liu
Mathematics 2025, 13(22), 3679; https://doi.org/10.3390/math13223679 - 17 Nov 2025
Viewed by 282
Abstract
In this paper, we study Cauchy problems for the semilinear parabolic equations ∂tu−▵u=G(u) with initial data in grand Herz spaces. We extend previous results established for classical Herz spaces to the broader framework [...] Read more.
In this paper, we study Cauchy problems for the semilinear parabolic equations ∂tu−▵u=G(u) with initial data in grand Herz spaces. We extend previous results established for classical Herz spaces to the broader framework of grand Herz spaces. The existence, uniqueness and stablity of solutions, as well as for their behaviour at small time are obtained by empolying heat kernel estimates, fixed-point theorems and some functional space theory. Full article
(This article belongs to the Special Issue Advances in Nonlinear Differential Equations with Applications)
15 pages, 369 KB  
Article
Certain Subclasses of Bi-Univalent Functions Involving Caputo Fractional Derivatives with Bounded Boundary Rotation
by Abbas Kareem Wanas, Mohammad El-Ityan, Adel Salim Tayyah and Adriana Catas
Mathematics 2025, 13(21), 3563; https://doi.org/10.3390/math13213563 - 6 Nov 2025
Viewed by 280
Abstract
In this paper, we introduce and investigate new subclasses of analytic bi-univalent functions defined via Caputo fractional derivatives with boundary rotation constraints. Utilizing the generalized operator Cȷϱ, which encompasses and extends classical operators such as the Salagean differential operator and [...] Read more.
In this paper, we introduce and investigate new subclasses of analytic bi-univalent functions defined via Caputo fractional derivatives with boundary rotation constraints. Utilizing the generalized operator Cȷϱ, which encompasses and extends classical operators such as the Salagean differential operator and the Libera–Bernardi integral operator, we establish sharp coefficient estimates for the initial Taylor Maclaurin coefficients of functions within these subclasses. Furthermore, we derive Fekete–Szegö-type inequalities that provide bounds on the second and third coefficients and their linear combinations involving a real parameter. Our approach leverages subordination principles through analytic functions associated with the classes Tς(ξ) and RΩȷ,ϱ(ϑ,ς,ξ), allowing a unified treatment of fractional differential operators in geometric function theory. The results generalize several known cases and open avenues for further exploration in fractional calculus applied to analytic function theory. Full article
(This article belongs to the Special Issue Advances in Nonlinear Differential Equations with Applications)
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