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Mathematics
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Nonlinear Functional Analysis and Its Applications 2021
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Nonlinear Functional Analysis and Its Applications 2021

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

Deadline for manuscript submissions: closed (1 May 2022) | Viewed by 7628

Special Issue Editor

Prof. Dr. Radu Precup

E-Mail Website
Guest Editor
Department of Mathematics, Babeş-Bolyai University, 400084 Cluj, Romania
Interests: nonlinear boundary value problems for ODEs and PDEs; theory of nonlinear operators; topological fixed point theory; critical point theory; mathematical modeling in biology and medicine
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues, 

Being concerned with nonlinear mappings in infinite dimensional spaces, Nonlinear Functional Analysis offers powerful tools and a unified framework for the investigation of numerous problems arising from the mathematical modeling of real-world processes. Also, the increase in complexity of those phenomena from science and society which are investigated by applied mathematicians leads to a continuous development of the theory.

This Special Issue invites original contributions, new developments of classical results, and advanced topics of high potential for future research and applications.

Potential topics include, but are not limited to:

  • Topological fixed point theory
  • Critical point theory
  • Equilibrium problems
  • Nonlinear ODEs and PDEs
  • Nonlinear models from physics, biology, and medicine

Prof. Dr. Radu Precup
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

  • nonlinear operators
  • topological degree theory
  • topological fixed point theory
  • critical point theory
  • variational methods
  • nonlinear boundary value problems

Published Papers (5 papers)

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Research

9 pages, 270 KiB  
Article
Multiple Periodic Solutions for Odd Perturbations of the Discrete Relativistic Operator
by Petru Jebelean and Călin Şerban
Mathematics 2022, 10(9), 1595; https://doi.org/10.3390/math10091595 - 08 May 2022
Cited by 1 | Viewed by 1085
Abstract
We obtain the existence of multiple pairs of periodic solutions for difference equations of type [...] Read more.
We obtain the existence of multiple pairs of periodic solutions for difference equations of type −Δ(Δu(n − 1)1 − |Δu(n − 1)|2)=λg(u(n))(n∈Z), where g:R→R is a continuous odd function with anticoercive primitive, and λ>0 is a real parameter. The approach is variational and relies on the critical point theory for convex, lower semicontinuous perturbations of C1-functionals. Full article
(This article belongs to the Special Issue Nonlinear Functional Analysis and Its Applications 2021)
13 pages, 301 KiB  
Article
On \({\mathbb{BID}}\)-Cone b-Metric Spaces over Banach Algebras: New Topological Properties and Fixed Point Theorems
by Huaping Huang, Wei-Shih Du and Jen-Yuan Chen
Mathematics 2022, 10(9), 1425; https://doi.org/10.3390/math10091425 - 23 Apr 2022
Viewed by 1047
Abstract
In this paper, we introduce the concepts of an inferior idempotent cone and a BID-cone b-metric space over Banach algebra. We establish some new existence theorems and fixed point theorems in the setting of complete BID-cone b-metric spaces over [...] Read more.
In this paper, we introduce the concepts of an inferior idempotent cone and a BID-cone b-metric space over Banach algebra. We establish some new existence theorems and fixed point theorems in the setting of complete BID-cone b-metric spaces over Banach algebra. Some fundamental questions and examples are also given. Full article
(This article belongs to the Special Issue Nonlinear Functional Analysis and Its Applications 2021)
6 pages, 228 KiB  
Article
On the Generalization of a Multiplicity Result
by Marek Galewski
Mathematics 2022, 10(6), 916; https://doi.org/10.3390/math10060916 - 13 Mar 2022
Viewed by 1191
Abstract
In this work, we shifted a recent multiplicity result by B. Ricceri from a Hilbert space to a Banach space setting by making use of a duality mapping relative to some increasing function. Using the min–max arguments, we provide conditions for an action [...] Read more.
In this work, we shifted a recent multiplicity result by B. Ricceri from a Hilbert space to a Banach space setting by making use of a duality mapping relative to some increasing function. Using the min–max arguments, we provide conditions for an action functional to have at least two global minima. Full article
(This article belongs to the Special Issue Nonlinear Functional Analysis and Its Applications 2021)
21 pages, 307 KiB  
Article
Fixed Point Results for Cirić and Almost Contractions in Convex b-Metric Spaces
by Savita Rathee, Anshuka Kadyan, Anil Kumar and Kenan Tas
Mathematics 2022, 10(3), 466; https://doi.org/10.3390/math10030466 - 31 Jan 2022
Cited by 2 | Viewed by 1945
Abstract
We establish a fixed point theorem for Cirić contraction in the context of convex b-metric spaces. Furthermore, we ensure that there is a fixed point for the maps satisfying the condition (B) (a kind of almost contraction) in convex b-metric spaces [...] Read more.
We establish a fixed point theorem for Cirić contraction in the context of convex b-metric spaces. Furthermore, we ensure that there is a fixed point for the maps satisfying the condition (B) (a kind of almost contraction) in convex b-metric spaces and demonstrate its uniqueness as well. Supporting examples to substantiate the generality of the proved results are given. Full article
(This article belongs to the Special Issue Nonlinear Functional Analysis and Its Applications 2021)
17 pages, 347 KiB  
Article
The Existence of Solutions for Local Dirichlet (r(u),s(u))-Problems
by Calogero Vetro
Mathematics 2022, 10(2), 237; https://doi.org/10.3390/math10020237 - 13 Jan 2022
Cited by 4 | Viewed by 1028
Abstract
In this paper, we consider local Dirichlet problems driven by the (r(u),s(u))-Laplacian operator in the principal part. We prove the existence of nontrivial weak solutions in the case where the variable exponents [...] Read more.
In this paper, we consider local Dirichlet problems driven by the (r(u),s(u))-Laplacian operator in the principal part. We prove the existence of nontrivial weak solutions in the case where the variable exponents r,s are real continuous functions and we have dependence on the solution u. The main contributions of this article are obtained in respect of: (i) Carathéodory nonlinearity satisfying standard regularity and polynomial growth assumptions, where in this case, we use geometrical and compactness conditions to establish the existence of the solution to a regularized problem via variational methods and the critical point theory; and (ii) Sobolev nonlinearity, somehow related to the space structure. In this case, we use a priori estimates and asymptotic analysis of regularized auxiliary problems to establish the existence and uniqueness theorems via a fixed-point argument. Full article
(This article belongs to the Special Issue Nonlinear Functional Analysis and Its Applications 2021)
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