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Axioms
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Recent Advances in Nonlinear Differential Equations: Theory, Methods and Applications
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Recent Advances in Nonlinear Differential Equations: Theory, Methods and Applications

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

Deadline for manuscript submissions: closed (30 December 2021) | Viewed by 11988

Special Issue Editors

Dr. Omar Bazighifan

E-Mail Website
Guest Editor
1. Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy
2. Department of Mathematics, Faculty of Science, Hadhramout University, Hadhramout 50512, Yemen
Interests: qualitative theory; ordinary differential equations; functional differential equations; dynamical systems; mathematical modeling
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Maria Alessandra Ragusa

E-Mail Website
Guest Editor
Department of Mathematics and Computer Science, University of Catania, 95124 Catania, Italy
Interests: linear and quasilinear differential equations of elliptic, parabolic, and ultraparabolic type in nondivergence and divergence form; Morrey spaces
Special Issues, Collections and Topics in MDPI journals
Dr. Fahd Jarad

E-Mail Website
Guest Editor
Department of Mathematics, Çankaya University, Etimesgut, Ankara 06790, Turkey
Interests: fractional calculus; Painleve analysis; fractional differential equations

Special Issue Information

Dear Colleagues,

Differential equations attract the attention of many modern researchers due to their usefulness in solving theoretical or applied problems.

The study of oscillatory phenomena is an important part of the theory of differential equations. Oscillations are relevant to virtually every area of applied science, including mechanics, electronics, radio engineering, and vibrotechnics.

This Special Issue welcomes high-quality papers with original research results in theoretical research and recent progress in the study of applied problems in science and technology.

Dr. Omar Bazighifan
Prof. Dr. Maria Alessandra Ragusa
Dr. Fahd Jarad
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

  • Qualitative properties of solutions
  • Oscillation theory
  • Approximation, stability, boundedness, periodicity, and asymptotic properties
  • Delay differential equations
  • Ordinary differential equations
  • Difference equations
  • Functional equations
  • Partial differential equations
  • Fractional, differential, and integral calculus
  • Applications

Published Papers (5 papers)

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Research

18 pages, 1602 KiB  
Article
Dynamical Analysis of a Predator-Prey Model Incorporating Predator Cannibalism and Refuge
by Maya Rayungsari, Agus Suryanto, Wuryansari Muharini Kusumawinahyu and Isnani Darti
Axioms 2022, 11(3), 116; https://doi.org/10.3390/axioms11030116 - 07 Mar 2022
Cited by 10 | Viewed by 2799
Abstract
We consider a mathematical model to describe the interaction between predator and prey that includes predator cannibalism and refuge. We aim to study the dynamics and its long-term behavior of the proposed model, as well as to discuss the effects of crucial parameters [...] Read more.
We consider a mathematical model to describe the interaction between predator and prey that includes predator cannibalism and refuge. We aim to study the dynamics and its long-term behavior of the proposed model, as well as to discuss the effects of crucial parameters associated with the model. We first show the boundedness and positivity of the solution of the model. Then, we study the existence and stability of all possible equilibrium points. The local stability of the model around each equilibrium point is studied via the linearized system, while the global stability is performed by defining a Lyapunov function. The model has four equilibrium points. It is found that the equilibrium point representing the extinction of both prey and predator populations is always unstable, while the other equilibrium points are conditionally stable. In addition, there is forward bifurcation phenomena that occur under certain condition. To support our analytical findings, we perform some numerical simulations. Full article
(This article belongs to the Special Issue Recent Advances in Nonlinear Differential Equations: Theory, Methods and Applications)
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14 pages, 330 KiB  
Article
Multiplicity Results of Solutions to Non-Local Magnetic Schrödinger–Kirchhoff Type Equations in RN
by Kisoeb Park
Axioms 2022, 11(2), 38; https://doi.org/10.3390/axioms11020038 - 19 Jan 2022
Cited by 1 | Viewed by 1888
Abstract
In this paper, we establish the existence of a nontrivial weak solution to Schrödinger-kirchhoff type equations with the fractional magnetic field without Ambrosetti and Rabinowitz condition using mountain pass theorem under a suitable assumption of the external force. Furthermore, we prove the existence [...] Read more.
In this paper, we establish the existence of a nontrivial weak solution to Schrödinger-kirchhoff type equations with the fractional magnetic field without Ambrosetti and Rabinowitz condition using mountain pass theorem under a suitable assumption of the external force. Furthermore, we prove the existence of infinitely many large- or small-energy solutions to this problem with Ambrosetti and Rabinowitz condition. The strategy of the proof for these results is to approach the problem by applying the variational methods, that is, the fountain and the dual fountain theorem with Cerami condition. Full article
(This article belongs to the Special Issue Recent Advances in Nonlinear Differential Equations: Theory, Methods and Applications)
18 pages, 2540 KiB  
Article
Chaotic Dynamics by Some Quadratic Jerk Systems
by Mei Liu, Bo Sang, Ning Wang and Irfan Ahmad
Axioms 2021, 10(3), 227; https://doi.org/10.3390/axioms10030227 - 14 Sep 2021
Cited by 11 | Viewed by 2260
Abstract
This paper is about the dynamical evolution of a family of chaotic jerk systems, which have different attractors for varying values of parameter a. By using Hopf bifurcation analysis, bifurcation diagrams, Lyapunov exponents, and cross sections, both self-excited and hidden attractors are [...] Read more.
This paper is about the dynamical evolution of a family of chaotic jerk systems, which have different attractors for varying values of parameter a. By using Hopf bifurcation analysis, bifurcation diagrams, Lyapunov exponents, and cross sections, both self-excited and hidden attractors are explored. The self-exited chaotic attractors are found via a supercritical Hopf bifurcation and period-doubling cascades to chaos. The hidden chaotic attractors (related to a subcritical Hopf bifurcation, and with a unique stable equilibrium) are also found via period-doubling cascades to chaos. A circuit implementation is presented for the hidden chaotic attractor. The methods used in this paper will help understand and predict the chaotic dynamics of quadratic jerk systems. Full article
(This article belongs to the Special Issue Recent Advances in Nonlinear Differential Equations: Theory, Methods and Applications)
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7 pages, 257 KiB  
Article
Stability of Weak Solutions to Parabolic Problems with Nonstandard Growth and Cross–Diffusion
by André H. Erhardt
Axioms 2021, 10(1), 14; https://doi.org/10.3390/axioms10010014 - 22 Jan 2021
Cited by 2 | Viewed by 1746
Abstract
We study the stability of a unique weak solution to certain parabolic systems with nonstandard growth condition, which are additionally dependent on a cross-diffusion term. More precisely, we show that two unique weak solutions of the considered system with different initial values are [...] Read more.
We study the stability of a unique weak solution to certain parabolic systems with nonstandard growth condition, which are additionally dependent on a cross-diffusion term. More precisely, we show that two unique weak solutions of the considered system with different initial values are controlled by their initial values. Full article
(This article belongs to the Special Issue Recent Advances in Nonlinear Differential Equations: Theory, Methods and Applications)
11 pages, 285 KiB  
Article
Oscillation of Emden–Fowler-Type Neutral Delay Differential Equations
by Shyam Sundar Santra, Taher A. Nofal, Hammad Alotaibi and Omar Bazighifan
Axioms 2020, 9(4), 136; https://doi.org/10.3390/axioms9040136 - 20 Nov 2020
Cited by 8 | Viewed by 1752
Abstract
In this work, we consider a type of second-order functional differential equations and establish qualitative properties of their solutions. These new results complement and improve a number of results reported in the literature. Finally, we provide an example that illustrates our results. Full article
(This article belongs to the Special Issue Recent Advances in Nonlinear Differential Equations: Theory, Methods and Applications)
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