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Mathematics
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Topological Methods in Nonlinear Analysis
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Topological Methods in Nonlinear Analysis

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Dynamical Systems".

Deadline for manuscript submissions: closed (31 October 2020) | Viewed by 8733

Special Issue Editor

Prof. Dr. Zdzisław Dzedzej

E-Mail Website
Guest Editor
Faculty of Applied Mathematics and Technical Physics, Gdańsk University of Technology, 80-233 Gdańsk, Poland
Interests: nonlinear analysis; fixed point theory; set-valued mappings; Conley index

Special Issue Information

Dear Colleagues,

The importance of nonlinear analysis in mathematics and applications is nowadays obvious, and there is still a growing number of new papers in this area. Topological methods have proven themselves to be very powerful tools in this area from the very beginning. We encourage you to submit research and review papers focused on both novelties in methods and applications in various areas of nonlinear mathematics. Both single-valued and set-valued operators are of interest, as well as special types of solutions of differential and integral equations and inclusions, symmetry properties, and similar phenomena, which can be treated by topological means. Results on the dynamic and asymptotic properties of solutions to ODE and PDE are also welcome.

Prof. Dr. Zdzisław Dzedzej
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

  • Fixed and periodic points
  • Degree theory
  • Measures of noncompactness
  • Nonsmooth analysis
  • Morse theory
  • Conley index
  • Mountain pass theorems
  • Borsuk–Ulam theorems
  • Variational methods
  • Bifurcation theory

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Published Papers (4 papers)

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Research

14 pages, 353 KiB  
Article
Ivanov’s Theorem for Admissible Pairs Applicable to Impulsive Differential Equations and Inclusions on Tori
by Jan Andres and Jerzy Jezierski
Mathematics 2020, 8(9), 1602; https://doi.org/10.3390/math8091602 - 17 Sep 2020
Cited by 7 | Viewed by 1990
Abstract
The main aim of this article is two-fold: (i) to generalize into a multivalued setting the classical Ivanov theorem about the lower estimate of a topological entropy in terms of the asymptotic Nielsen numbers, and (ii) to apply the related inequality for admissible [...] Read more.
The main aim of this article is two-fold: (i) to generalize into a multivalued setting the classical Ivanov theorem about the lower estimate of a topological entropy in terms of the asymptotic Nielsen numbers, and (ii) to apply the related inequality for admissible pairs to impulsive differential equations and inclusions on tori. In case of a positive topological entropy, the obtained result can be regarded as a nontrivial contribution to deterministic chaos for multivalued impulsive dynamics. Full article
(This article belongs to the Special Issue Topological Methods in Nonlinear Analysis)
14 pages, 308 KiB  
Article
Generalized Gradient Equivariant Multivalued Maps, Approximation and Degree
by Zdzisław Dzedzej and Tomasz Gzella
Mathematics 2020, 8(8), 1262; https://doi.org/10.3390/math8081262 - 1 Aug 2020
Cited by 2 | Viewed by 1599
Abstract
Consider the Euclidean space Rn with the orthogonal action of a compact Lie group G. We prove that a locally Lipschitz G-invariant mapping f from Rn to R can be uniformly approximated by G-invariant smooth mappings g in [...] Read more.
Consider the Euclidean space Rn with the orthogonal action of a compact Lie group G. We prove that a locally Lipschitz G-invariant mapping f from Rn to R can be uniformly approximated by G-invariant smooth mappings g in such a way that the gradient of g is a graph approximation of Clarkés generalized gradient of f. This result enables a proper development of equivariant gradient degree theory for a class of set-valued gradient mappings. Full article
(This article belongs to the Special Issue Topological Methods in Nonlinear Analysis)
12 pages, 780 KiB  
Article
A Fixed-Point Approach to the Hyers–Ulam Stability of Caputo–Fabrizio Fractional Differential Equations
by Kui Liu, Michal Fečkan and JinRong Wang
Mathematics 2020, 8(4), 647; https://doi.org/10.3390/math8040647 - 22 Apr 2020
Cited by 12 | Viewed by 2974
Abstract
In this paper, we study Hyers–Ulam and Hyers–Ulam–Rassias stability of nonlinear Caputo–Fabrizio fractional differential equations on a noncompact interval. We extend the corresponding uniqueness and stability results on a compact interval. Two examples are given to illustrate our main results. Full article
(This article belongs to the Special Issue Topological Methods in Nonlinear Analysis)
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8 pages, 246 KiB  
Article
A Topological Coincidence Theory for Multifunctions via Homotopy
by Donal O’Regan
Mathematics 2020, 8(3), 427; https://doi.org/10.3390/math8030427 - 16 Mar 2020
Cited by 1 | Viewed by 1500
Abstract
A new simple result is presented which immediately yields the topological transversality theorem for coincidences. Full article
(This article belongs to the Special Issue Topological Methods in Nonlinear Analysis)
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