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Mathematics
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Nonlinear Equations: Theory, Methods, and Applications III
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Nonlinear Equations: Theory, Methods, and Applications III

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

Deadline for manuscript submissions: 30 June 2024 | Viewed by 7092

Special Issue Editors

Prof. Dr. Ravi P. Agarwal

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Guest Editor
Department of Mathematics, Texas A and M University-Kingsville, Kingsville, TX 78363, USA
Interests: boundary value problems; nonlinear analysis; differential and difference equations; fixed point theory; general inequalities
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Bashir Ahmad

E-Mail Website
Guest Editor
Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
Interests: differential equations; boundary value problems; nonlinear analysis; applications
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

It is our pleasure to announce the launch of a new Special Issue of Mathematics on the topic of “Nonlinear Equations: Theory, Methods, and Applications II”. While the list below is by no means exclusive, some of the topics we would be interested in covering in this Special Issue include:

  • Ordinary differential equations;
  • Delay differential equations;
  • Functional equations;
  • Equations on time scales;
  • Partial differential equations;
  • Fractional differential equations;
  • Stochastic differential equations;
  • Integral equations;
  • Applications of fixed-point theorems to nonlinear equations.

We look forward to your contributions.

Prof. Dr. Ravi P. Agarwal
Prof. Dr. Bashir Ahmad
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. 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.

Published Papers (7 papers)

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Research

19 pages, 342 KiB  
Article
Existence of Solutions for Planar Kirchhoff–Choquard Problems
by Rui Niu and Tianxing Wu
Mathematics 2023, 11(17), 3754; https://doi.org/10.3390/math11173754 - 31 Aug 2023
Viewed by 593
Abstract
In this article, we are interested in the study of the following Kirchhoff–Choquard equations: [...] Read more.
In this article, we are interested in the study of the following Kirchhoff–Choquard equations: −a+b∫R2|∇u|2dxΔu+V(x)u=λ(ln|x|∗u2)u+f(u),x∈R2, where λ>0,a>0,b>0, V and f are continuous functions with some appropriate assumptions. We prove that when the parameter λ is sufficiently small, the above problem has a mountain pass solution, a least energy solution and a ground state solution by applying the variational methods and building some subtle inequalities. Full article
(This article belongs to the Special Issue Nonlinear Equations: Theory, Methods, and Applications III)
14 pages, 292 KiB  
Article
Bounded Solutions of Semi-Linear Parabolic Differential Equations with Unbounded Delay Terms
by Allaberen Ashyralyev and Sa’adu Bello Mu’azu
Mathematics 2023, 11(16), 3470; https://doi.org/10.3390/math11163470 - 10 Aug 2023
Viewed by 492
Abstract
In the present work, an initial boundary value problem (IBVP) for the semi-linear delay differential equation in a Banach space with unbounded positive operators is studied. The main theorem on the uniqueness and existence of a bounded solution (BS) of this problem is [...] Read more.
In the present work, an initial boundary value problem (IBVP) for the semi-linear delay differential equation in a Banach space with unbounded positive operators is studied. The main theorem on the uniqueness and existence of a bounded solution (BS) of this problem is established. The application of the main theorem to four different semi-linear delay parabolic differential equations is presented. The first- and second-order accuracy difference schemes (FSADSs) for the solution of a one-dimensional semi-linear time-delay parabolic equation are considered. The new desired numerical results of this paper and their discussion are presented. Full article
(This article belongs to the Special Issue Nonlinear Equations: Theory, Methods, and Applications III)
26 pages, 407 KiB  
Article
Towards a Proof of Bahri–Coron’s Type Theorem for Mixed Boundary Value Problems
by Azeb Alghanemi, Slim Chaabane, Hichem Chtioui and Abdellahi Soumaré
Mathematics 2023, 11(8), 1955; https://doi.org/10.3390/math11081955 - 20 Apr 2023
Viewed by 885
Abstract
We consider a nonlinear variational elliptic problem with critical nonlinearity on a bounded domain of Rn,n≥3 and mixed Dirichlet–Neumann boundary conditions. We study the effect of the domain’s topology on the existence of solutions as Bahri–Coron did in [...] Read more.
We consider a nonlinear variational elliptic problem with critical nonlinearity on a bounded domain of Rn,n≥3 and mixed Dirichlet–Neumann boundary conditions. We study the effect of the domain’s topology on the existence of solutions as Bahri–Coron did in their famous work on the homogeneous Dirichlet problem. However, due to the influence of the part of the boundary where the Neumann condition is prescribed, the blow-up picture in the present setting is more complicated and makes the mixed boundary problems different with respect to the homogeneous ones. Such complexity imposes modification of the argument of Bahri–Coron and demands new constructions and extra ideas. Full article
(This article belongs to the Special Issue Nonlinear Equations: Theory, Methods, and Applications III)
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12 pages, 274 KiB  
Article
Qualitative Properties of Solutions to a Class of Sixth-Order Equations
by Cristian-Paul Danet
Mathematics 2023, 11(6), 1280; https://doi.org/10.3390/math11061280 - 07 Mar 2023
Viewed by 1002
Abstract
In this paper, we present a detailed study of a class of sixth-order semilinear PDEs: existence, regularity and uniqueness. The uniqueness results are a consequence of a maximum principle called the P-function method. Full article
(This article belongs to the Special Issue Nonlinear Equations: Theory, Methods, and Applications III)
11 pages, 265 KiB  
Article
On Some Error Bounds for Milne’s Formula in Fractional Calculus
by Muhammad Aamir Ali, Zhiyue Zhang and Michal Fečkan
Mathematics 2023, 11(1), 146; https://doi.org/10.3390/math11010146 - 28 Dec 2022
Cited by 5 | Viewed by 1434
Abstract
In this paper, we found the error bounds for one of the open Newton–Cotes formulas, namely Milne’s formula for differentiable convex functions in the framework of fractional and classical calculus. We also give some mathematical examples to show that the newly established bounds [...] Read more.
In this paper, we found the error bounds for one of the open Newton–Cotes formulas, namely Milne’s formula for differentiable convex functions in the framework of fractional and classical calculus. We also give some mathematical examples to show that the newly established bounds are valid for Milne’s formula. Full article
(This article belongs to the Special Issue Nonlinear Equations: Theory, Methods, and Applications III)
11 pages, 993 KiB  
Article
Solitary Wave Solutions for the Stochastic Fractional-Space KdV in the Sense of the M-Truncated Derivative
by Wael W. Mohammed, Clemente Cesarano, Farah M. Al-Askar and Mahmoud El-Morshedy
Mathematics 2022, 10(24), 4792; https://doi.org/10.3390/math10244792 - 16 Dec 2022
Cited by 5 | Viewed by 1111
Abstract
The stochastic fractional-space Korteweg–de Vries equation (SFSKdVE) in the sense of the M-truncated derivative is examined in this article. In the Itô sense, the SFSKdVE is forced by multiplicative white noise. To produce new trigonometric, hyperbolic, rational, and elliptic stochastic fractional solutions, the [...] Read more.
The stochastic fractional-space Korteweg–de Vries equation (SFSKdVE) in the sense of the M-truncated derivative is examined in this article. In the Itô sense, the SFSKdVE is forced by multiplicative white noise. To produce new trigonometric, hyperbolic, rational, and elliptic stochastic fractional solutions, the tanh–coth and Jacobi elliptic function methods are used. The obtained solutions are useful in interpreting certain fascinating physical phenomena because the KdV equation is essential for understanding the behavior of waves in shallow water. To demonstrate how the multiplicative noise and the M-truncated derivative impact the precise solutions of the SFSKdVE, different 3D and 2D graphical representations are plotted. Full article
(This article belongs to the Special Issue Nonlinear Equations: Theory, Methods, and Applications III)
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14 pages, 317 KiB  
Article
On Solvability of Fractional (p,q)-Difference Equations with (p,q)-Difference Anti-Periodic Boundary Conditions
by Ravi P. Agarwal, Hana Al-Hutami and Bashir Ahmad
Mathematics 2022, 10(23), 4419; https://doi.org/10.3390/math10234419 - 23 Nov 2022
Cited by 1 | Viewed by 745
Abstract
We discuss the solvability of a (p,q)-difference equation of fractional order α∈(1,2], equipped with anti-periodic boundary conditions involving the first-order (p,q)-difference operator. The desired results are [...] Read more.
We discuss the solvability of a (p,q)-difference equation of fractional order α∈(1,2], equipped with anti-periodic boundary conditions involving the first-order (p,q)-difference operator. The desired results are accomplished with the aid of standard fixed point theorems. Examples are presented for illustrating the obtained results. Full article
(This article belongs to the Special Issue Nonlinear Equations: Theory, Methods, and Applications III)
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