Special Issue "Nonlinear Differential Equations and Dynamical Systems: Theory and Applications"

A special issue of Axioms (ISSN 2075-1680).

Deadline for manuscript submissions: 30 September 2020.

Special Issue Editors

Prof. Dr. Feliz Manuel Minhós
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Guest Editor
Departamento de Matemática, Escola de Ciências e Tecnologia, Centro de Investigação em Matemática e Aplicações (CIMA), Instituto de Investigação e Formação Avançada, Universidade de Évora, Rua Romão Ramalho, 59, 7000-671 Évora, Portugal
Interests: differential and difference equations; boundary value problems; topological and variational methods
Special Issues and Collections in MDPI journals
Prof. Dr. João Fialho
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Guest Editor
British University Vietnam, CDC Building, 25-27 Le Dai Hanh, Le Dai Hanh Ward, Hai Ba Trung District, 10000 Ha Noi, Vietnam
Interests: differential and difference equations; boundary value problems; topological and variational methods, mathematical modelling
Special Issues and Collections in MDPI journals

Special Issue Information

Dear Colleagues,

Nonlinear differential equations, dynamical systems, and related topics are particularly trendy topics at present, as they have had wide and significant applications in many fields of Physics, Chemistry, Engineering, Biology or even Economics, in general, and Mathematics, in particular.

In addition, they can be approached using several different methods and techniques. As examples, we can refer to variational and topological methods, fixed point theory, initial and boundary value problems, continuous and discrete dynamical systems, qualitative theory, stability theory, the existence and control of chaos, and the existence of attractors and periodic orbits, among others.

In this Special Issue we propose to collect some state-of-the-art results that can contribute effectively to these areas.

Before submission authors should carefully read over the journal's instructions for Authors, in https://www.mdpi.com/journal/axioms/instructions

Prof. Dr. Feliz Manuel Minhós
Prof. Dr. João Fialho
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 papers will be 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 quarterly 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 1000 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 and integral equations
  • Initial and boundary value problems
  • Fractional calculus and applications
  • Variational and topological methods
  • Qualitative, asymptotic and oscillation properties
  • Fixed point theory
  • Continuous and discrete dynamical systems
  • Stability theory
  • Chaos theory and chaos control
  • Existence of periodic orbits and attractors
  • Applications to real world phenomena

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Published Papers (6 papers)

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Research

Open AccessArticle
Asymptotic Properties of Neutral Differential Equations with Variable Coefficients
Axioms 2020, 9(3), 96; https://doi.org/10.3390/axioms9030096 - 12 Aug 2020
Abstract
The aim of this work is to study oscillatory behavior of solutions for even-order neutral nonlinear differential equations. By using the Riccati substitution, a new oscillation conditions is obtained which insures that all solutions to the studied equation are oscillatory. The obtained results [...] Read more.
The aim of this work is to study oscillatory behavior of solutions for even-order neutral nonlinear differential equations. By using the Riccati substitution, a new oscillation conditions is obtained which insures that all solutions to the studied equation are oscillatory. The obtained results complement the well-known oscillation results present in the literature. Some example are illustrated to show the applicability of the obtained results. Full article
Open AccessArticle
On the Uniqueness Classes of Solutions of Boundary Value Problems for Third-Order Equations of the Pseudo-Elliptic Type
Axioms 2020, 9(3), 80; https://doi.org/10.3390/axioms9030080 - 16 Jul 2020
Abstract
The paper is devoted to solutions of the third order pseudo-elliptic type equations. An energy estimates for solutions of the equations considering transformation’s character of the body form were established by using of an analog of the Saint-Venant principle. In consequence of this [...] Read more.
The paper is devoted to solutions of the third order pseudo-elliptic type equations. An energy estimates for solutions of the equations considering transformation’s character of the body form were established by using of an analog of the Saint-Venant principle. In consequence of this estimate, the uniqueness theorems were obtained for solutions of the first boundary value problem for third order equations in unlimited domains. The energy estimates are illustrated on two examples. Full article
Open AccessArticle
Boundary Value Problem for Weak Nonlinear Partial Differential Equations of Mixed Type with Fractional Hilfer Operator
Axioms 2020, 9(2), 68; https://doi.org/10.3390/axioms9020068 - 17 Jun 2020
Abstract
In this paper, we consider a boundary value problem for a nonlinear partial differential equation of mixed type with Hilfer operator of fractional integro-differentiation in a positive rectangular domain and with spectral parameter in a negative rectangular domain. With respect to the first [...] Read more.
In this paper, we consider a boundary value problem for a nonlinear partial differential equation of mixed type with Hilfer operator of fractional integro-differentiation in a positive rectangular domain and with spectral parameter in a negative rectangular domain. With respect to the first variable, this equation is a nonlinear fractional differential equation in the positive part of the considering segment and is a second-order nonlinear differential equation with spectral parameter in the negative part of this segment. Using the Fourier series method, the solutions of nonlinear boundary value problems are constructed in the form of a Fourier series. Theorems on the existence and uniqueness of the classical solution of the problem are proved for regular values of the spectral parameter. For irregular values of the spectral parameter, an infinite number of solutions of the mixed equation in the form of a Fourier series are constructed. Full article
Open AccessArticle
On the Solvability of Nonlinear Third-Order Two-Point Boundary Value Problems
Axioms 2020, 9(2), 62; https://doi.org/10.3390/axioms9020062 - 31 May 2020
Abstract
Under barrier strips type assumptions we study the existence of C 3 [ 0 , 1 ] —solutions to various two-point boundary value problems for the equation x = f ( t , x , x , x ) . [...] Read more.
Under barrier strips type assumptions we study the existence of C 3 [ 0 , 1 ] —solutions to various two-point boundary value problems for the equation x = f ( t , x , x , x ) . We give also some results guaranteeing positive or non-negative, monotone, convex or concave solutions. Full article
Open AccessArticle
Initial Value Problem For Nonlinear Fractional Differential Equations With ψ-Caputo Derivative Via Monotone Iterative Technique
Axioms 2020, 9(2), 57; https://doi.org/10.3390/axioms9020057 - 21 May 2020
Abstract
In this article, we discuss the existence and uniqueness of extremal solutions for nonlinear initial value problems of fractional differential equations involving the ψ -Caputo derivative. Moreover, some uniqueness results are obtained. Our results rely on the standard tools of functional analysis. More [...] Read more.
In this article, we discuss the existence and uniqueness of extremal solutions for nonlinear initial value problems of fractional differential equations involving the ψ -Caputo derivative. Moreover, some uniqueness results are obtained. Our results rely on the standard tools of functional analysis. More precisely we apply the monotone iterative technique combined with the method of upper and lower solutions to establish sufficient conditions for existence as well as the uniqueness of extremal solutions to the initial value problem. An illustrative example is presented to point out the applicability of our main results. Full article
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Open AccessArticle
Sufficient Conditions for Oscillation of Fourth-Order Neutral Differential Equations with Distributed Deviating Arguments
Axioms 2020, 9(2), 39; https://doi.org/10.3390/axioms9020039 - 11 Apr 2020
Cited by 1
Abstract
Some new sufficient conditions are established for the oscillation of fourth order neutral differential equations with continuously distributed delay of the form r t N x t α + a b q t , ϑ x β δ t , [...] Read more.
Some new sufficient conditions are established for the oscillation of fourth order neutral differential equations with continuously distributed delay of the form r t N x t α + a b q t , ϑ x β δ t , ϑ d ϑ = 0 , where t t 0 and N x t : = x t + p t x φ t . An example is provided to show the importance of these results. Full article
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