Special Issue "Advances in Nonlinear Spectral Theory"

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

Deadline for manuscript submissions: 31 December 2020.

Special Issue Editor

Prof. Raffaele Chiappinelli
Website
Guest Editor
Department of Information Engineering and Mathematical Sciences, University of Siena, 53100 Siena, Italy
Interests: nonlinear functional analysis; nonlinear operators; nonlinear eigenvalue problems; nonlinear spectral theory

Special Issue Information

Dear Colleagues,

Since its appearance in the late Sixties of the last Century, the spectral theory of nonlinear operators acting in Banach spaces has made many advances, and in various different directions, including the applications of the theory itself to boundary value problems for ordinary and partial differential equations. Discovering the similarities and the differences existing with the realm of bounded linear operators, known to us from linear functional analysis, is an active and exciting field of research, so much if we deal with nonlinear perturbations of linear operators.

Nonlinear Spectral Theory is closely related to (and in a sense contains properly) the extremely vast and popular field of Nonlinear Eigenvalue Problems, and as such it employs and develops practically all methods of nonlinear analysis, notably Fixed point theory, Degree theory and topological methods, Bifurcation theory, Non-compact operators, Minimization methods and critical point theory for gradient operators, as well as the applications of these methods to differential equations.

This Special Issue of the Journal Mathematics aims at collecting new ideas, methods and/or specific results (but also well organized reviews of known results) from any researcher sharing the interest in the field and working in the areas cited above, or nearby.

Prof. Raffaele Chiappinelli
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 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. Mathematics is an international peer-reviewed open access monthly 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 1200 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 eigenvalue problems
  • Degree theory and topological methods
  • Abstract bifurcation theory
  • Non-compact operators
  • Variational methods for nonlinear operators
  • Critical point theory

Published Papers (1 paper)

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Research

Open AccessArticle
Large Constant-Sign Solutions of Discrete Dirichlet Boundary Value Problems with p-Mean Curvature Operator
Mathematics 2020, 8(3), 381; https://doi.org/10.3390/math8030381 - 09 Mar 2020
Abstract
In this paper, we consider the existence of infinitely many large constant-sign solutions for a discrete Dirichlet boundary value problem involving p -mean curvature operator. The methods are based on the critical point theory and truncation techniques. Our results are obtained by requiring [...] Read more.
In this paper, we consider the existence of infinitely many large constant-sign solutions for a discrete Dirichlet boundary value problem involving p -mean curvature operator. The methods are based on the critical point theory and truncation techniques. Our results are obtained by requiring appropriate oscillating behaviors of the non-linear term at infinity, without any symmetry assumptions. Full article
(This article belongs to the Special Issue Advances in Nonlinear Spectral Theory)
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