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Qualitative Analysis of Differential Equations: Theory and Applications
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Qualitative Analysis of Differential Equations: Theory and Applications

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 13384

Special Issue Editors

Dr. Osman Tunç

E-Mail Website
Guest Editor
Department of Computer Programing, Baskale Vocational School, Van Yuzuncu Yil University, Van 65080, Turkey
Interests: ordinary differential equations; functional differential equations; integro-differential equations; applied mathematics
Prof. Dr. Vitalii Slynko

E-Mail Website
Guest Editor
Institute of Mathematics, University of Wuerzburg, Emil-Fischer-Str., 40, 97074 Wuerzburg, Germany
Interests: zero-solution; Lyapunov function; parabolic systems; switched systems; average dwell time; nonlinear dynamics; fuzzy differential equations; fuzzy numbers; differentiability
Prof. Dr. Sandra Pinelas

E-Mail Website
Guest Editor
Departamento De Ciencias Exatas E Engenharia Academia Militar, Av. Conde Castro Guimaraes, 2720-113 Amadora, Portugal
Interests: differential equations; difference equations; oscillatory behavior; asymptotic behavior
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

In the past year, qualitative analyses, i.e., analyses of the stability, boundedness, integrability, existence and uniqueness  of solutions  of functional differential equations (delay differential equations, neutral differential equations, advanced differential equations and  impulsive differential equations); dynamic models; integral equations; integro-differential equations; partial  differential equations; fractional differential equations; fractional integro-differential equations; fractional partial  differential equations; etc., have attracted the attention of numerous researchers at the theoretical level and at the level of their applications. From the relevant literature, it can be observed that numerous processes and problems in biology, the interactions between species, population dynamics, microbiology, distributed networks, mechanics, medicine, nuclear reactors, chemistry, distributed networks, epidemiology, physics, engineering, economics, physiology, viscoelasticity, etc. can be modelled mathematically by these kind of equations.

Therefore, these kind of equations have vital, important roles in real world applications. However, these kind of equations can be solved analytically in particular cases, but not numerically. Qualitative theory can enable us to obtain information about the behaviour of solutions without prior information on them by means of Lyapunov’s second method, the fixed-point method, the Lyapunov–Krasovskii method, and so on. The aim of this SI is to collect some new theoretical contributions and real-world applications with regard to the qualitative theory of  the equations mentioned above. 

Dr. Osman Tunç
Prof. Dr. Vitalii Slynko
Prof. Dr. Sandra Pinelas
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.

Keywords

  • qualitative theory
  • qualitative analysis
  • ordinary differential equations
  • partial differential equations
  • functional differential equations (delay differential equations, neutral differential equations, advanced differential equations, and impulsive differential equations)
  • integral equations
  • integro-differential equations
  • fractional calculus
  • fractional differential equations
  • fractional integral equations
  • fractional integro-differential equations
  • fractional partial differential equations
  • fractional partial integro-differential equations
  • dynamical models of integer orders
  • dynamical models of fractional orders
  • Lyapunov’s second method
  • fixed-point method
  • Lyapunov–Krasovskii method
  • control theory
  • stabilization
  • real-world applications
  • numerical simulations

Published Papers (16 papers)

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Research

15 pages, 290 KiB  
Article
New Results on the Ulam–Hyers–Mittag–Leffler Stability of Caputo Fractional-Order Delay Differential Equations
by Osman Tunç
Mathematics 2024, 12(9), 1342; https://doi.org/10.3390/math12091342 (registering DOI) - 28 Apr 2024
Viewed by 96
Abstract
The author considers a nonlinear Caputo fractional-order delay differential equation (CFrDDE) with multiple variable delays. First, we study the existence and uniqueness of the solutions of the CFrDDE with multiple variable delays. Second, we obtain two new results on the Ulam–Hyers–Mittag–Leffler (UHML) stability [...] Read more.
The author considers a nonlinear Caputo fractional-order delay differential equation (CFrDDE) with multiple variable delays. First, we study the existence and uniqueness of the solutions of the CFrDDE with multiple variable delays. Second, we obtain two new results on the Ulam–Hyers–Mittag–Leffler (UHML) stability of the same equation in a closed interval using the Picard operator, Chebyshev norm, Bielecki norm and the Banach contraction principle. Finally, we present three examples to show the applications of our results. Although there is an extensive literature on the Lyapunov, Ulam and Mittag–Leffler stability of fractional differential equations (FrDEs) with and without delays, to the best of our knowledge, there are very few works on the UHML stability of FrDEs containing a delay. Thereby, considering a CFrDDE containing multiple variable delays and obtaining new results on the existence and uniqueness of the solutions and UHML stability of this kind of CFrDDE are the important aims of this work. Full article
(This article belongs to the Special Issue Qualitative Analysis of Differential Equations: Theory and Applications)
11 pages, 281 KiB  
Article
Boundedness of Vector Linéard Equation with Multiple Variable Delays
by Melek Gözen
Mathematics 2024, 12(5), 769; https://doi.org/10.3390/math12050769 - 04 Mar 2024
Viewed by 406
Abstract
In this article, we consider a system of ordinary differential equations (ODEs) of second order with two variable time delays. We obtain new conditions for uniform ultimate bounded (UUB) solutions of the considered system. The technique of the proof is based on the [...] Read more.
In this article, we consider a system of ordinary differential equations (ODEs) of second order with two variable time delays. We obtain new conditions for uniform ultimate bounded (UUB) solutions of the considered system. The technique of the proof is based on the Lyapunov–Krasovskii functional (LKF) method using a new LKF. The main result of this article extends and improves a recent result for ODEs of second order with a constant delay to a more general system of ODEs of second order with two variable time delays. In this particular case, we also give a numerical example to verify the application of the main result of this article. Full article
(This article belongs to the Special Issue Qualitative Analysis of Differential Equations: Theory and Applications)
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13 pages, 269 KiB  
Article
New Results on Ulam Stabilities of Nonlinear Integral Equations
by Osman Tunç, Cemil Tunç and Jen-Chih Yao
Mathematics 2024, 12(5), 682; https://doi.org/10.3390/math12050682 - 26 Feb 2024
Cited by 1 | Viewed by 467
Abstract
This article deals with the study of Hyers–Ulam stability (HU stability) and Hyers–Ulam–Rassias stability (HUR stability) for two classes of nonlinear Volterra integral equations (VIEqs), which are Hammerstein-type integral and Hammerstein-type functional integral equations, respectively. In this article, both the HU stability and [...] Read more.
This article deals with the study of Hyers–Ulam stability (HU stability) and Hyers–Ulam–Rassias stability (HUR stability) for two classes of nonlinear Volterra integral equations (VIEqs), which are Hammerstein-type integral and Hammerstein-type functional integral equations, respectively. In this article, both the HU stability and HUR stability are obtained for the first integral equation and the HUR stability is obtained for the second integral equation. Among the used techniques, we present fixed point arguments and the Gronwall lemma as a basic tool. Two supporting examples are also provided to demonstrate the applications and effectiveness of the results. Full article
(This article belongs to the Special Issue Qualitative Analysis of Differential Equations: Theory and Applications)
16 pages, 290 KiB  
Article
Global Existence and Uniqueness of Solutions of Integral Equations with Multiple Variable Delays and Integro Differential Equations: Progressive Contractions
by Osman Tunç, Cemil Tunç and Jen-Chih Yao
Mathematics 2024, 12(2), 171; https://doi.org/10.3390/math12020171 - 05 Jan 2024
Cited by 1 | Viewed by 602
Abstract
In this work, we delve into a nonlinear integral equation (IEq) with multiple variable time delays and a nonlinear integro-differential equation (IDEq) without delay. Global existence and uniqueness (GEU) of solutions of that IEq with multiple variable time delays and IDEq are investigated [...] Read more.
In this work, we delve into a nonlinear integral equation (IEq) with multiple variable time delays and a nonlinear integro-differential equation (IDEq) without delay. Global existence and uniqueness (GEU) of solutions of that IEq with multiple variable time delays and IDEq are investigated by the fixed point method using progressive contractions, which are due to T.A. Burton. We prove four new theorems including sufficient conditions with regard to GEU of solutions of the equations. The results generalize and improve some related published results of the relevant literature. Full article
(This article belongs to the Special Issue Qualitative Analysis of Differential Equations: Theory and Applications)
17 pages, 374 KiB  
Article
Dynamics of a Higher-Order Three-Dimensional Nonlinear System of Difference Equations
by Murad Khan Hassani, Yasin Yazlik, Nouressadat Touafek, Mohammed Salah Abdelouahab, Mouataz Billah Mesmouli and Fatma E. Mansour
Mathematics 2024, 12(1), 16; https://doi.org/10.3390/math12010016 (registering DOI) - 20 Dec 2023
Viewed by 608
Abstract
In this paper, we study the semi-cycle analysis of positive solutions and the asymptotic behavior of positive solutions of three-dimensional system of difference equations with a higher order under certain parametric conditions. Furthermore, we show the boundedness and persistence, the rate of convergence [...] Read more.
In this paper, we study the semi-cycle analysis of positive solutions and the asymptotic behavior of positive solutions of three-dimensional system of difference equations with a higher order under certain parametric conditions. Furthermore, we show the boundedness and persistence, the rate of convergence of the solutions and the global asymptotic stability of the unique equilibrium point of the proposed system under certain parametric conditions. Finally, for this system, we offer some numerical examples which support our analytical results. Full article
(This article belongs to the Special Issue Qualitative Analysis of Differential Equations: Theory and Applications)
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9 pages, 254 KiB  
Article
Conditions for the Oscillation of Solutions to Neutral Differential Equations of Higher Order
by Maryam Al-Kandari
Mathematics 2023, 11(24), 4909; https://doi.org/10.3390/math11244909 - 09 Dec 2023
Viewed by 617
Abstract
In this research, we applied three techniques—the comparison technique, the Riccati technique, and the integral averages technique to analyze and establish various conditions and properties associated with the oscillatory behavior of even-order neutral differential equations. These findings contribute to a better understanding of [...] Read more.
In this research, we applied three techniques—the comparison technique, the Riccati technique, and the integral averages technique to analyze and establish various conditions and properties associated with the oscillatory behavior of even-order neutral differential equations. These findings contribute to a better understanding of the dynamics of such equations. To demonstrate the efficacy of these new conditions and properties, we present illustrative examples. This study offers valuable insights into the behavior of neutral differential equations, advancing our knowledge in this field. Full article
(This article belongs to the Special Issue Qualitative Analysis of Differential Equations: Theory and Applications)
10 pages, 282 KiB  
Article
A Time-Fractional Parabolic Inequality on a Bounded Interval
by Amal Alshabanat, Eman Almoalim, Mohamed Jleli and Bessem Samet
Mathematics 2023, 11(24), 4892; https://doi.org/10.3390/math11244892 - 06 Dec 2023
Viewed by 712
Abstract
We study a time-fractional parabolic inequality posed on a bounded interval and involving a wight function W, where the fractional derivative is considered in the Caputo sense. We establish a general condition ensuring that the set of weak solutions is empty. Next, [...] Read more.
We study a time-fractional parabolic inequality posed on a bounded interval and involving a wight function W, where the fractional derivative is considered in the Caputo sense. We establish a general condition ensuring that the set of weak solutions is empty. Next, some particular cases of the weight function W are discussed. Full article
(This article belongs to the Special Issue Qualitative Analysis of Differential Equations: Theory and Applications)
23 pages, 859 KiB  
Article
Bifurcation Behavior and Hybrid Controller Design of a 2D Lotka–Volterra Commensal Symbiosis System Accompanying Delay
by Qingyi Cui, Changjin Xu, Wei Ou, Yicheng Pang, Zixin Liu, Peiluan Li and Lingyun Yao
Mathematics 2023, 11(23), 4808; https://doi.org/10.3390/math11234808 - 28 Nov 2023
Cited by 14 | Viewed by 616
Abstract
All the time, differential dynamical models with delay has witness a tremendous application value in characterizing the internal law among diverse biological populations in biology. In the current article, on the basis of the previous publications, we formulate a new Lotka–Volterra commensal symbiosis [...] Read more.
All the time, differential dynamical models with delay has witness a tremendous application value in characterizing the internal law among diverse biological populations in biology. In the current article, on the basis of the previous publications, we formulate a new Lotka–Volterra commensal symbiosis system accompanying delay. Utilizing fixed point theorem, inequality tactics and an appropriate function, we gain the sufficient criteria on existence and uniqueness, non-negativeness and boundedness of the solution to the formulated delayed Lotka–Volterra commensal symbiosis system. Making use of stability and bifurcation theory of delayed differential equation, we focus on the emergence of bifurcation behavior and stability nature of the formulated delayed Lotka–Volterra commensal symbiosis system. A new delay-independent stability and bifurcation conditions on the model are presented. By constructing a positive definite function, we explore the global stability. By constructing two diverse hybrid delayed feedback controllers, we can adjusted the domain of stability and time of appearance of Hopf bifurcation of the delayed Lotka–Volterra commensal symbiosis system. The effect of time delay on the domain of stability and time of appearance of Hopf bifurcation of the model is given. Matlab experiment diagrams are provided to sustain the acquired key outcomes. Full article
(This article belongs to the Special Issue Qualitative Analysis of Differential Equations: Theory and Applications)
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28 pages, 1189 KiB  
Article
Mathematical and Stability Analysis of Dengue–Malaria Co-Infection with Disease Control Strategies
by Azhar Iqbal Kashif Butt, Muhammad Imran, Brett A. McKinney, Saira Batool and Hassan Aftab
Mathematics 2023, 11(22), 4600; https://doi.org/10.3390/math11224600 - 09 Nov 2023
Cited by 1 | Viewed by 1090
Abstract
Historically, humans have been infected by mosquito-borne diseases, including dengue fever and malaria fever. There is an urgent need for comprehensive methods in the prevention, control, and awareness of the hazards posed by dengue and malaria fever to public health. We propose a [...] Read more.
Historically, humans have been infected by mosquito-borne diseases, including dengue fever and malaria fever. There is an urgent need for comprehensive methods in the prevention, control, and awareness of the hazards posed by dengue and malaria fever to public health. We propose a new mathematical model for dengue and malaria co-infection with the aim of comprehending disease dynamics better and developing more efficient control strategies in light of the threat posed to public health by co-infection. The proposed mathematical model comprises four time-dependent vector population classes (SEIdIm) and seven host population classes (SEIdImIdmTR). First, we show that the proposed model is well defined by proving that it is bounded and positive in a feasible region. We further identify the equilibrium states of the model, including disease-free and endemic equilibrium points, where we perform stability analysis at equilibrium points. Then, we determine the reproduction number R0 to measure the level of disease containment. We perform a sensitivity analysis of the model’s parameters to identify the most critical ones for potential control strategies. We also prove that the proposed model is well posed. Finally, the article examines three distinct co-infection control measures, including spraying or killing vectors, taking precautions for one’s own safety, and reducing the infectious contact between the host and vector populations. The control analysis of the proposed model reveals that all control parameters are effective in disease control. However, self-precaution is the most effective and accessible method, and the reduction of the vector population through spraying is the second most effective strategy to implement. Disease eradication is attainable as the vector population decreases. The effectiveness of the implemented strategies is also illustrated with the help of graphs. Full article
(This article belongs to the Special Issue Qualitative Analysis of Differential Equations: Theory and Applications)
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12 pages, 282 KiB  
Article
Existence and Uniqueness of Positive Solutions for Semipositone Lane-Emden Equations on the Half-Axis
by Imed Bachar
Mathematics 2023, 11(19), 4184; https://doi.org/10.3390/math11194184 - 06 Oct 2023
Viewed by 476
Abstract
Semipositone Lane–Emden type equations are considered on the half-axis. Such equations have been used in modelling several phenomena in astrophysics and mathematical physics and are often difficult to solve analytically. We provide sufficient conditions for the existence of a positive continuous solution and [...] Read more.
Semipositone Lane–Emden type equations are considered on the half-axis. Such equations have been used in modelling several phenomena in astrophysics and mathematical physics and are often difficult to solve analytically. We provide sufficient conditions for the existence of a positive continuous solution and we describe its global behavior. Our approach is based on a perturbed operator technique and fixed point theorems. Some examples are presented to illustrate the main results. Full article
(This article belongs to the Special Issue Qualitative Analysis of Differential Equations: Theory and Applications)
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15 pages, 320 KiB  
Article
An Improved Approach to Investigate the Oscillatory Properties of Third-Order Neutral Differential Equations
by Osama Moaaz and Yousef Alnafisah
Mathematics 2023, 11(10), 2290; https://doi.org/10.3390/math11102290 - 15 May 2023
Viewed by 862
Abstract
In this work, by considering a third-order differential equation with delay-neutral arguments, we investigate the oscillatory behavior of solutions. It is known that the relationships between the solution and its derivatives of different orders, as well as between the solution and its corresponding [...] Read more.
In this work, by considering a third-order differential equation with delay-neutral arguments, we investigate the oscillatory behavior of solutions. It is known that the relationships between the solution and its derivatives of different orders, as well as between the solution and its corresponding function, can help to obtain more efficient oscillation criteria for differential equations of neutral type. So, we deduce some new relationships of an iterative nature. Then, we test the effect of these relationships on the criteria that exclude positive solutions to the studied equation. By comparing our results with previous results in the literature, we show the importance and novelty of the new results. Full article
(This article belongs to the Special Issue Qualitative Analysis of Differential Equations: Theory and Applications)
29 pages, 1545 KiB  
Article
Design and Analysis of a New COVID-19 Model with Comparative Study of Control Strategies
by Azhar Iqbal Kashif Butt, Saira Batool, Muhammad Imran and Muneerah Al Nuwairan
Mathematics 2023, 11(9), 1978; https://doi.org/10.3390/math11091978 - 22 Apr 2023
Cited by 8 | Viewed by 1244
Abstract
The COVID-19 pandemic has become a worldwide concern and has caused great frustration in the human community. Governments all over the world are struggling to combat the disease. In an effort to understand and address the situation, we conduct a thorough study of [...] Read more.
The COVID-19 pandemic has become a worldwide concern and has caused great frustration in the human community. Governments all over the world are struggling to combat the disease. In an effort to understand and address the situation, we conduct a thorough study of a COVID-19 model that provides insights into the dynamics of the disease. For this, we propose a new LSHSEAIHR COVID-19 model, where susceptible populations are divided into two sub-classes: low-risk susceptible populations, LS, and high-risk susceptible populations, HS. The aim of the subdivision of susceptible populations is to construct a model that is more reliable and realistic for disease control. We first prove the existence of a unique solution to the purposed model with the help of fundamental theorems of functional analysis and show that the solution lies in an invariant region. We compute the basic reproduction number and describe constraints that ensure the local and global asymptotic stability at equilibrium points. A sensitivity analysis is also carried out to identify the model’s most influential parameters. Next, as a disease transmission control technique, a class of isolation is added to the intended LSHSEAIHR model. We suggest simple fixed controls through the adjustment of quarantine rates as a first control technique. To reduce the spread of COVID-19 as well as to minimize the cost functional, we constitute an optimal control problem and develop necessary conditions using Pontryagin’s maximum principle. Finally, numerical simulations with and without controls are presented to demonstrate the efficiency and efficacy of the optimal control approach. The optimal control approach is also compared with an approach where the state model is solved numerically with different time-independent controls. The numerical results, which exhibit dynamical behavior of the COVID-19 system under the influence of various parameters, suggest that the implemented strategies, particularly the quarantine of infectious individuals, are effective in significantly reducing the number of infected individuals and achieving herd immunity. Full article
(This article belongs to the Special Issue Qualitative Analysis of Differential Equations: Theory and Applications)
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18 pages, 993 KiB  
Article
Finite-Element Method for the Simulation of Lipid Vesicle/Fluid Interactions in a Quasi–Newtonian Fluid Flow
by Aymen Laadhari
Mathematics 2023, 11(8), 1950; https://doi.org/10.3390/math11081950 - 20 Apr 2023
Cited by 2 | Viewed by 910
Abstract
We present a computational framework for modeling an inextensible single vesicle driven by the Helfrich force in an incompressible, non-Newtonian extracellular Carreau fluid. The vesicle membrane is captured with a level set strategy. The local inextensibility constraint is relaxed by introducing a penalty [...] Read more.
We present a computational framework for modeling an inextensible single vesicle driven by the Helfrich force in an incompressible, non-Newtonian extracellular Carreau fluid. The vesicle membrane is captured with a level set strategy. The local inextensibility constraint is relaxed by introducing a penalty which allows computational savings and facilitates implementation. A high-order Galerkin finite element approximation allows accurate calculations of the membrane force with high-order derivatives. The time discretization is based on the double composition of the one-step backward Euler scheme, while the time step size is flexibly controlled using a time integration error estimation. Numerical examples are presented with particular attention paid to the validation and assessment of the model’s relevance in terms of physiological significance. Optimal convergence rates of the time discretization are obtained. Full article
(This article belongs to the Special Issue Qualitative Analysis of Differential Equations: Theory and Applications)
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17 pages, 1069 KiB  
Article
On System of Variable Order Nonlinear p-Laplacian Fractional Differential Equations with Biological Application
by Hasib Khan, Jehad Alzabut, Haseena Gulzar, Osman Tunç and Sandra Pinelas
Mathematics 2023, 11(8), 1913; https://doi.org/10.3390/math11081913 - 18 Apr 2023
Cited by 16 | Viewed by 1482
Abstract
The study of variable order differential equations is important in science and engineering for a better representation and analysis of dynamical problems. In the literature, there are several fractional order operators involving variable orders. In this article, we construct a nonlinear variable order [...] Read more.
The study of variable order differential equations is important in science and engineering for a better representation and analysis of dynamical problems. In the literature, there are several fractional order operators involving variable orders. In this article, we construct a nonlinear variable order fractional differential system with a p-Laplacian operator. The presumed problem is a general class of the nonlinear equations of variable orders in the ABC sense of derivatives in combination with Caputo’s fractional derivative. We investigate the existence of solutions and the Hyers–Ulam stability of the considered equation. The presumed problem is a hybrid in nature and has a lot of applications. We have given its particular example as a waterborne disease model of variable order which is analysed for the numerical computations for different variable orders. The results obtained for the variable orders have an advantage over the constant orders in that the variable order simulations present the fluctuation of the real dynamics throughout our observations of the simulations. Full article
(This article belongs to the Special Issue Qualitative Analysis of Differential Equations: Theory and Applications)
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21 pages, 674 KiB  
Article
Global Dynamics for Competition between Two Wolbachia Strains with Bidirectional Cytoplasmic Incompatibility
by Qiming Huang, Lijie Chang, Zhaowang Zhang and Bo Zheng
Mathematics 2023, 11(7), 1691; https://doi.org/10.3390/math11071691 - 01 Apr 2023
Viewed by 970
Abstract
Releasing Wolbachia-infected mosquitoes to suppress or replace wild vector mosquitoes has been carried out in 24 countries worldwide, showing great promise in controlling mosquitoes and mosquito-borne diseases. To face the instability of Wolbachia infection in different environments during the area-wide application, we [...] Read more.
Releasing Wolbachia-infected mosquitoes to suppress or replace wild vector mosquitoes has been carried out in 24 countries worldwide, showing great promise in controlling mosquitoes and mosquito-borne diseases. To face the instability of Wolbachia infection in different environments during the area-wide application, we should consider the overlapping of two Wolbachia strains. In this case, bidirectional cytoplasmic incompatibility occurs, which results in mating partners infected with exclusive Wolbachia strains producing inviable offspring. To determine the better Wolbachia candidate for release, we develop an ordinary differential equation model to study the global dynamics for competition between two Wolbachia strains. Our theoretical results on the sharp estimate of stable curves completely determine the fate of the two Wolbachia strains, which help choose appropriate strains for release. Full article
(This article belongs to the Special Issue Qualitative Analysis of Differential Equations: Theory and Applications)
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11 pages, 289 KiB  
Article
Oscillatory Properties of Fourth-Order Advanced Differential Equations
by Alanoud Almutairi, Ali Hasan Ali, Omar Bazighifan and Loredana Florentina Iambor
Mathematics 2023, 11(6), 1391; https://doi.org/10.3390/math11061391 - 13 Mar 2023
Cited by 1 | Viewed by 906
Abstract
This paper presents a study on the oscillatory behavior of solutions to fourth-order advanced differential equations involving p-Laplacian-like operator. We obtain oscillation criteria using techniques from first and second-order delay differential equations. The results of this work contribute to a deeper understanding [...] Read more.
This paper presents a study on the oscillatory behavior of solutions to fourth-order advanced differential equations involving p-Laplacian-like operator. We obtain oscillation criteria using techniques from first and second-order delay differential equations. The results of this work contribute to a deeper understanding of fourth-order differential equations and their connections to various branches of mathematics and practical sciences. The findings emphasize the importance of continued research in this area. Full article
(This article belongs to the Special Issue Qualitative Analysis of Differential Equations: Theory and Applications)
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