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Mathematics
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Qualitative Analysis of Differential, Difference, and Dynamic Equations and Applications
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Qualitative Analysis of Differential, Difference, and Dynamic Equations 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: closed (23 December 2019) | Viewed by 11754

Special Issue Editor

Prof. Dr. Yuriy Rogovchenko

E-Mail Website
Guest Editor
Department of Mathematical Sciences, University of Agder, P.O. Box 422, N-4604 Kristiansand, Norway
Interests: qualitative theory of ordinary, functional, and impulsive differential equations; mathematical modelling in medicine, biology and life sciences; undergraduate mathematics education
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

We cordially invite submissions to the special issue of Mathematics, an open access journal published monthly online by MDPI. This Special Issue on Qualitative Analysis of Differential, Difference, and Dynamic Equations and Applications will feature high quality invited and contributed papers addressing most recent developments in the field.

The list of topics covered by the special issue includes but is not limited to the following important aspects of the qualitative theory of differential, functional differential, difference, and dynamic equations:

  • Asymptotic behavior of solutions
  • Oscillation and nonoscillation of solutions
  • Stability of solutions, instability, and bifurcations
  • Existence of bounded and periodic solutions and their properties
  • Uniqueness and multiplicity of solutions
  • Applications to engineering, economics, medicine, life and social sciences

The Editor  of this Special Issue on Qualitative Analysis of Differential, Difference, and Dynamic Equations and Applications and the editorial stuff of the journal Mathematics warmly welcome original research papers addressing important theoretical issues as well as comprehensive papers surveying recent developments in the area. We are particularly interested in receiving submissions featuring applications of theoretical methods and ideas to mathematical modelling of phenomena and processes arising in engineering, economics, life and social sciences.

We look forward to receiving your valuable research papers for this special issue!

Prof. Dr. Yuriy Rogovchenko
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. 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

  • Differential, functional differential, difference, and dynamic equations
  • Asymptotic behavior
  • Oscillatory and non-oscillatory solutions
  • Stability and bifurcations
  • Existence, uniqueness, and multiplicity of solutions
  • Bounded and periodic solutions
  • Mathematical modelling and applications

Published Papers (5 papers)

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Research

11 pages, 276 KiB  
Article
Constant Sign Solutions to Linear Fractional Integral Problems and Their Applications to the Monotone Method
by Daniel Cao Labora and Rosana Rodríguez-López
Mathematics 2020, 8(2), 156; https://doi.org/10.3390/math8020156 - 22 Jan 2020
Cited by 1 | Viewed by 1339
Abstract
This manuscript provides some results concerning the sign of solutions for linear fractional integral equations with constant coefficients. This information is later used to prove the existence of solutions to some nonlinear problems, together with underestimates and overestimates. These results are obtained after [...] Read more.
This manuscript provides some results concerning the sign of solutions for linear fractional integral equations with constant coefficients. This information is later used to prove the existence of solutions to some nonlinear problems, together with underestimates and overestimates. These results are obtained after applying suitable modifications in the classical process of monotone iterative techniques. Finally, we provide an example where we prove the existence of solutions, and we compute some estimates. Full article
(This article belongs to the Special Issue Qualitative Analysis of Differential, Difference, and Dynamic Equations and Applications)
9 pages, 273 KiB  
Article
Solvability of Coupled Systems of Generalized Hammerstein-Type Integral Equations in the Real Line
by Feliz Minhós and Robert de Sousa
Mathematics 2020, 8(1), 111; https://doi.org/10.3390/math8010111 - 10 Jan 2020
Cited by 4 | Viewed by 2171
Abstract
In this work, we consider a generalized coupled system of integral equations of Hammerstein-type with, eventually, discontinuous nonlinearities. The main existence tool is Schauder’s fixed point theorem in the space of bounded and continuous functions with bounded and continuous derivatives on R , [...] Read more.
In this work, we consider a generalized coupled system of integral equations of Hammerstein-type with, eventually, discontinuous nonlinearities. The main existence tool is Schauder’s fixed point theorem in the space of bounded and continuous functions with bounded and continuous derivatives on R , combined with the equiconvergence at ± ∞ to recover the compactness of the correspondent operators. To the best of our knowledge, it is the first time where coupled Hammerstein-type integral equations in real line are considered with nonlinearities depending on several derivatives of both variables and, moreover, the derivatives can be of different order on each variable and each equation. On the other hand, we emphasize that the kernel functions can change sign and their derivatives in order to the first variable may be discontinuous. The last section contains an application to a model to study the deflection of a coupled system of infinite beams. Full article
(This article belongs to the Special Issue Qualitative Analysis of Differential, Difference, and Dynamic Equations and Applications)
38 pages, 503 KiB  
Article
Functional Separation of Variables in Nonlinear PDEs: General Approach, New Solutions of Diffusion-Type Equations
by Andrei D. Polyanin
Mathematics 2020, 8(1), 90; https://doi.org/10.3390/math8010090 - 6 Jan 2020
Cited by 12 | Viewed by 3420
Abstract
The study gives a brief overview of existing modifications of the method of functional separation of variables for nonlinear PDEs. It proposes a more general approach to the construction of exact solutions to nonlinear equations of applied mathematics and mathematical physics, based on [...] Read more.
The study gives a brief overview of existing modifications of the method of functional separation of variables for nonlinear PDEs. It proposes a more general approach to the construction of exact solutions to nonlinear equations of applied mathematics and mathematical physics, based on a special transformation with an integral term and the generalized splitting principle. The effectiveness of this approach is illustrated by nonlinear diffusion-type equations that contain reaction and convective terms with variable coefficients. The focus is on equations of a fairly general form that depend on one, two or three arbitrary functions (such nonlinear PDEs are most difficult to analyze and find exact solutions). A lot of new functional separable solutions and generalized traveling wave solutions are described (more than 30 exact solutions have been presented in total). It is shown that the method of functional separation of variables can, in certain cases, be more effective than (i) the nonclassical method of symmetry reductions based on an invariant surface condition, and (ii) the method of differential constraints based on a single differential constraint. The exact solutions obtained can be used to test various numerical and approximate analytical methods of mathematical physics and mechanics. Full article
(This article belongs to the Special Issue Qualitative Analysis of Differential, Difference, and Dynamic Equations and Applications)
12 pages, 261 KiB  
Article
Oscillatory Properties of Third-Order Neutral Delay Differential Equations with Noncanonical Operators
by George E. Chatzarakis, Jozef Džurina and Irena Jadlovská
Mathematics 2019, 7(12), 1177; https://doi.org/10.3390/math7121177 - 3 Dec 2019
Cited by 22 | Viewed by 2080
Abstract
In the paper, we study the oscillatory and asymptotic properties of solutions to a class of third-order linear neutral delay differential equations with noncanonical operators. Via the application of comparison principles with associated first and second-order delay differential inequalities, we offer new criteria [...] Read more.
In the paper, we study the oscillatory and asymptotic properties of solutions to a class of third-order linear neutral delay differential equations with noncanonical operators. Via the application of comparison principles with associated first and second-order delay differential inequalities, we offer new criteria for the oscillation of all solutions to a given differential equation. Our technique essentially simplifies the process of investigation and reduces the number of conditions required in previously known results. The strength of the newly obtained results is illustrated on the Euler type equations. Full article
(This article belongs to the Special Issue Qualitative Analysis of Differential, Difference, and Dynamic Equations and Applications)
15 pages, 1095 KiB  
Article
Dynamic Analysis of a Pest Management Smith Model with Impulsive State Feedback Control and Continuous Delay
by Zhenzhen Shi, Yaning Li and Huidong Cheng
Mathematics 2019, 7(7), 591; https://doi.org/10.3390/math7070591 - 1 Jul 2019
Cited by 13 | Viewed by 2373
Abstract
In our paper, we propose a single population Smith model with continuous delay and impulsive state feedback control. The application in pest management of this model is investigated. First, the singularity of this model is qualitatively analyzed; then, we consider the existence and [...] Read more.
In our paper, we propose a single population Smith model with continuous delay and impulsive state feedback control. The application in pest management of this model is investigated. First, the singularity of this model is qualitatively analyzed; then, we consider the existence and uniqueness of order-one periodic orbit in order to determine the frequency of the implementation of chemical control. Moreover, based on the limit method of the sequences of subsequent points, we verify the stability of periodic orbit to ensure a certain robustness of this control; at last, we carry out the numerical simulations to verify the correctness of the theoretical results. Full article
(This article belongs to the Special Issue Qualitative Analysis of Differential, Difference, and Dynamic Equations and Applications)
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