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Mathematics
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Mathematical Analysis and Boundary Value Problems II
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Mathematical Analysis and Boundary Value Problems II

A special issue of Mathematics (ISSN 2227-7390).

Deadline for manuscript submissions: closed (31 December 2022) | Viewed by 4888

Special Issue Editors

Prof. Dr. Alberto Cabada

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Guest Editor
Facultade de Matemáticas, Campus Vida, 15782 Santiago de Compostela, Galicia, Spain
Interests: ordinary differential equations; boundary value problems; Green's functions; comparison results; nonlinear analysis
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. José Ángel Cid

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Guest Editor
Departamento de Matemáticas, Universidade de Vigo, Campus de Ourense, 32004 Ourense, Spain
Interests: differential equations; ordinary differential equations; mathematical analysis
Special Issues, Collections and Topics in MDPI journals
Dr. Lucía López-Somoza

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Guest Editor
Departamento de Estatística, Análise Matemática e Optimización Instituto de Matemáticas, Facultade de Matemáticas, Universidade de Santiago de Compostela, Santiago de Compostela, 15782 Galicia, Spain
Interests: differential equations; boundary value problems; mathematical analysis
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The study of the existence, nonexistence, and the uniqueness of solutions of boundary value problems, coupled to its stability, plays a fundamental role in the research of different kinds of differential equations (ordinary, fractional, and partial). One of the main tools developed in this area consists of fixed point theory and critical point theory.

The aim of this Special Issue is to study this type of problem in a broad sense. The development of theories that ensure the existence of solutions via topological or variational methods will contribute to the enrichment of this topic and will broaden the knowledge of this area.

This issue is a continuation of the previous successful Special Issue “Mathematical Analysis and Boundary Value Problems”.

Prof. Dr. Alberto Cabada
Prof. Dr. José Ángel Cid
Dr. Lucía López-Somoza
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

  • boundary value problems
  • comparison principles
  • ordinary differential equations
  • stability theory
  • fractional differential equations
  • topological methods in differential equations
  • variational methods
  • fixed point theory
  • critical point theory

Published Papers (3 papers)

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Research

18 pages, 342 KiB  
Article
Bifurcation-Type Results for the Fractional p-Laplacian with Parametric Nonlinear Reaction
by Silvia Frassu and Antonio Iannizzotto
Mathematics 2023, 11(2), 491; https://doi.org/10.3390/math11020491 - 16 Jan 2023
Viewed by 912
Abstract
We consider a nonlinear, nonlocal elliptic equation driven by the degenerate fractional p-Laplacian with a Dirichlet boundary condition and involving a parameter λ>0. The reaction is of general type, including concave–convex reactions as a special case. By means of [...] Read more.
We consider a nonlinear, nonlocal elliptic equation driven by the degenerate fractional p-Laplacian with a Dirichlet boundary condition and involving a parameter λ>0. The reaction is of general type, including concave–convex reactions as a special case. By means of variational methods and truncation techniques, we prove that there exists λ* such that the problem has two positive solutions for λ<λ*, one solution for λ=λ*, and no solutions for λ>λ*. Full article
(This article belongs to the Special Issue Mathematical Analysis and Boundary Value Problems II)
11 pages, 285 KiB  
Article
Monotone Iterative Technique for a New Class of Nonlinear Sequential Fractional Differential Equations with Nonlinear Boundary Conditions under the ψ-Caputo Operator
by Zidane Baitiche, Choukri Derbazi, Mouffak Benchohra and Juan J. Nieto
Mathematics 2022, 10(7), 1173; https://doi.org/10.3390/math10071173 - 04 Apr 2022
Cited by 4 | Viewed by 1316
Abstract
The main crux of this work is to study the existence of extremal solutions for a new class of nonlinear sequential fractional differential equations (NSFDEs) with nonlinear boundary conditions (NBCs) under the ψ-Caputo operator. The obtained outcomes of the proposed problem are [...] Read more.
The main crux of this work is to study the existence of extremal solutions for a new class of nonlinear sequential fractional differential equations (NSFDEs) with nonlinear boundary conditions (NBCs) under the ψ-Caputo operator. The obtained outcomes of the proposed problem are derived by means of the monotone iterative technique (MIT) associated with the method of upper and lower solutions. Lastly, the desired findings are well illustrated by an example. Full article
(This article belongs to the Special Issue Mathematical Analysis and Boundary Value Problems II)
17 pages, 388 KiB  
Article
Two-Field Weak Solutions for a Class of Contact Models
by Andaluzia Matei and Madalina Osiceanu
Mathematics 2022, 10(3), 369; https://doi.org/10.3390/math10030369 - 25 Jan 2022
Cited by 5 | Viewed by 1635
Abstract
Two contact models are considered, with the behavior of the materials being described by a constitutive law governed by the subdifferential of a convex map. We deliver variational formulations based on the theory of bipotentials. In this approach, the unknowns are pairs consisting [...] Read more.
Two contact models are considered, with the behavior of the materials being described by a constitutive law governed by the subdifferential of a convex map. We deliver variational formulations based on the theory of bipotentials. In this approach, the unknowns are pairs consisting of the displacement field and the Cauchy stress tensor. The two-field weak solutions are sought into product spaces involving variable convex sets. Both models lead to variational systems which can be cast in an abstract setting. After delivering some abstract results, we apply them in order to study the weak solvability of the mechanical models as well as the data dependence of the weak solutions. Full article
(This article belongs to the Special Issue Mathematical Analysis and Boundary Value Problems II)
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