Special Issue "New Trends on Boundary Value Problems"

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

Deadline for manuscript submissions: 31 July 2021.

Special Issue Editors

Prof. Dr. Miklós Rontó
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Guest Editor
University of Miskolc, Department of Analysis, 3515 Miskolc-Egyetemváros, Miskolc, Hungary
Interests: Functional differential equations; boundary value problems; numerical-analytic methods; theory of positive operators
Prof. Dr. András Rontó
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Guest Editor
Institute of Mathematics, Czech Academy of Sciences
Interests: Functional differential equations; boundary value problems; numerical-analytic methods; theory of positive operators
Special Issues and Collections in MDPI journals
Prof. Dr. Nino Partsvania
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Guest Editor
A. Razmadze Mathematical Institute of I. Javakhishvili Tbilisi State University, Tbilisi, Georgia
Interests: functional differential equations; boundary value problems; oscillation theory
Prof. Dr. Bedřich Půža
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Guest Editor
Faculty of Business and Management, Institute of Informatics, Head of department, Kolejní 2906/4, Královo Pole, 61200, Brno, Česká republika
Prof. Dr. Hriczó Krisztián
E-Mail Website
Guest Editor
Department of Analysis, Institute of Mathematics, University of Miskolc, Miskolc 3515, Hungary
Interests: Applied mathematical; Differential equations
Special Issues and Collections in MDPI journals

Special Issue Information

Dear Colleagues,

Boundary-value problems form a very important chapter of the theory of differential equations. It is commonly known that they occur in modelling of various phenomena in applied sciences. On the other hand, results and techniques arising in boundary-value problems are of much theoretical interest due to their close relation to other areas (e.g., the connection between the sign-constancy of Green's operator and oscillatory properties of the equation).

This Special Issue is devoted to nonlinear boundary-value problems in a broad sense, and will cover results on ordinary and functional differential equations, with a special emphasis on new and original
methods for the analysis of various boundary-value problems, including those specific to equations with argument deviations. Topics include but are not limited to solvability analysis; the approximate
construction of solutions; and the existence of positive solutions for problems with periodic, antiperiodic, multipoint, and other types of boundary conditions.

We hope that contributions to this Issue will be of interest to many researchers working in boundary-value problems and functional differential equations, and will stimulate further progress in the field.

Prof. Dr. Miklós Rontó
Prof. Dr. András Rontó
Prof. Dr. Nino Partsvania
Prof. Dr. Bedřich Půža
Prof. Dr. Hriczó Krisztián
Guest Editors

Manuscript Submission Information

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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 1600 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 boundary-value problems
  • Local and nonlocal boundary conditions
  • Numerical-analytic methods
  • Functional-differential equations
  • Approximate solutions
  • Successive approximations

Published Papers (3 papers)

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Research

Article
First Solution of Fractional Bioconvection with Power Law Kernel for a Vertical Surface
Mathematics 2021, 9(12), 1366; https://doi.org/10.3390/math9121366 - 12 Jun 2021
Viewed by 210
Abstract
The present study provides the heat transfer analysis of a viscous fluid in the presence of bioconvection with a Caputo fractional derivative. The unsteady governing equations are solved by Laplace after using a dimensional analysis approach subject to the given constraints on the [...] Read more.
The present study provides the heat transfer analysis of a viscous fluid in the presence of bioconvection with a Caputo fractional derivative. The unsteady governing equations are solved by Laplace after using a dimensional analysis approach subject to the given constraints on the boundary. The impact of physical parameters can be seen through a graphical illustration. It is observed that the maximum decline in bioconvection and velocity can be attained for smaller values of the fractional parameter. The fractional approach can be very helpful in controlling the boundary layers of the fluid properties for different values of time. Additionally, it is observed that the model obtained with generalized constitutive laws predicts better memory than the model obtained with artificial replacement. Further, these results are compared with the existing literature to verify the validity of the present results. Full article
(This article belongs to the Special Issue New Trends on Boundary Value Problems)
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Article
Analysis and Computation of Solutions for a Class of Nonlinear SBVPs Arising in Epitaxial Growth
Mathematics 2021, 9(7), 774; https://doi.org/10.3390/math9070774 - 02 Apr 2021
Viewed by 292
Abstract
In this work, the existence and nonexistence of stationary radial solutions to the elliptic partial differential equation arising in the molecular beam epitaxy are studied. Since we are interested in radial solutions, we focus on the fourth-order singular ordinary differential equation. It is [...] Read more.
In this work, the existence and nonexistence of stationary radial solutions to the elliptic partial differential equation arising in the molecular beam epitaxy are studied. Since we are interested in radial solutions, we focus on the fourth-order singular ordinary differential equation. It is non-self adjoint, it does not have exact solutions, and it admits multiple solutions. Here, λR measures the intensity of the flux and G is stationary flux. The solution depends on the size of the parameter λ. We use a monotone iterative technique and integral equations along with upper and lower solutions to prove that solutions exist. We establish the qualitative properties of the solutions and provide bounds for the values of the parameter λ, which help us to separate existence from nonexistence. These results complement some existing results in the literature. To verify the analytical results, we also propose a new computational iterative technique and use it to verify the bounds on λ and the dependence of solutions for these computed bounds on λ. Full article
(This article belongs to the Special Issue New Trends on Boundary Value Problems)
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Article
Nonlocal Sequential Boundary Value Problems for Hilfer Type Fractional Integro-Differential Equations and Inclusions
Mathematics 2021, 9(6), 615; https://doi.org/10.3390/math9060615 - 15 Mar 2021
Cited by 2 | Viewed by 264
Abstract
In the present research, we study boundary value problems for fractional integro-differential equations and inclusions involving the Hilfer fractional derivative. Existence and uniqueness results are obtained by using the classical fixed point theorems of Banach, Krasnosel’skiĭ, and Leray–Schauder in the single-valued case, while [...] Read more.
In the present research, we study boundary value problems for fractional integro-differential equations and inclusions involving the Hilfer fractional derivative. Existence and uniqueness results are obtained by using the classical fixed point theorems of Banach, Krasnosel’skiĭ, and Leray–Schauder in the single-valued case, while Martelli’s fixed point theorem, a nonlinear alternative for multivalued maps, and the Covitz–Nadler fixed point theorem are used in the inclusion case. Examples are presented to illustrate our results. Full article
(This article belongs to the Special Issue New Trends on Boundary Value Problems)
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