Small perturbations for nonlinear Schrödinger equations with magnetic potential
type: Item
instance of: scholarly article
title: Small perturbations for nonlinear Schrödinger equations with magnetic potential
zbMATH Open document ID: 1465.35366
author: Youpei Zhang
author: Vicenţiu D. Rădulescu
author: X. H. Tang
published in: Milan Journal of Mathematics
publication date: 2021-05-25T00:00:00Z
review text: In this paper, the authors study the qualitative analysis of solutions for three classes of nonlinear problems driven by the magnetic Laplace operator, where two equations are studied on bounded domains (under Dirichlet boundary condition) while the third problem is on the entire Euclidean space. They deduced that if a certain perturbation is sufficiently small in a prescribed sense, then the problems have at least two distinct solutions in a related magnetic Sobolev space. The proofs is based on variational, topological and analytic methods.
Mathematics Subject Classification ID: 35Q55
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 58E05
Mathematics Subject Classification ID: 44A10
Mathematics Subject Classification ID: 35B33
Mathematics Subject Classification ID: 35B20
Mathematics Subject Classification ID: 49M41
Mathematics Subject Classification ID: 35A15
Mathematics Subject Classification ID: 35A16
zbMATH DE Number: 7350892
zbMATH Keywords: magnetic Laplace operator
zbMATH Keywords: compactness
zbMATH Keywords: magnetic Sobolev space
zbMATH Keywords: perturbation
zbMATH Keywords: constrained minimization
zbMATH Keywords: multiple solutions
reviewed by: Jiqiang Zheng
MaRDI profile type: Publication
full work available at URL: s00032-020-00322-7
OpenAlex ID: W3094776040
cites work: Multiple Solutions for a Nonlinear Schrödinger Equation with Magnetic Fields
cites work: Multiple solutions for a semilinear elliptic equation with critical growth and magnetic field
cites work: Dual variational methods in critical point theory and applications
cites work: A semilinear Schrödinger equation in the presence of a magnetic field
cites work: Topological results on a certain class of functionals and application
cites work: A Perturbation Method in Critical Point Theory and Applications
cites work: Q4748596
cites work: A Relation Between Pointwise Convergence of Functions and Convergence of Functionals
cites work: Positive solutions of nonlinear elliptic equations involving critical sobolev exponents
cites work: Multiple solutions of degenerate perturbed elliptic problems involving a subcritical Sobolev exponent
cites work: Multiple solutions to a nonlinear Schrödinger equation with Aharonov-Bohm magnetic potential
cites work: Q3480488
cites work: Multi-bump solutions for the nonlinear magnetic Schrödinger equation with exponential critical growth in \(\mathbb{R}^2 \)
cites work: Multiplicity and concentration of solutions to the nonlinear magnetic Schrödinger equation
cites work: Perturbations of embedded eigenvalues for a magnetic Schrödinger operator on a cylinder
cites work: Hardy inequalities for Landau Hamiltonian and for Baouendi-Grushin operator with Aharonov-Bohm type magnetic field. Part I
cites work: Q3310242
cites work: Nonlinear Analysis - Theory and Methods
cites work: Q3079717
cites work: Q3749777
cites work: Critical singular problems on infinite cones.
cites work: Infinitely many critical points for functionals which are not even and applications to superlinear boundary value problems
cites work: Variational Methods
cites work: Minimax theorems
DOI: 10.1007/S00032-020-00322-7
description: scientific article; zbMATH DE number 7350892