Concentration phenomena for nonlinear magnetic Schrödinger equations with critical growth
type: Item
instance of: scholarly article
title: Concentration phenomena for nonlinear magnetic Schrödinger equations with critical growth
zbMATH Open document ID: 1465.35140
author: Chao Ji
author: Vicenţiu D. Rădulescu
published in: Israel Journal of Mathematics
publication date: 2021-04-29T00:00:00Z
review text: The paper is concerned with nonlinear magnetic Schrödinger equations involving critical growth of the form \[ \begin{cases} \left(\frac{\varepsilon}{i}\nabla - A(x) \right)^2u+V(x)u=f\left(|u|^2\right)u+|u|^{2^*-2}u \quad\text{in }\mathbb{R}^N,\\ u\in H^1\left(\mathbb{R}^N; \mathbb{C}\right), \end{cases} \] where \(\varepsilon>0\) is a parameter, \(N \geq 3\), \(2^*=\frac{2N}{N-2}\) is the critical Sobolev exponent, \(V: \mathbb{R}^N\to\mathbb{R}\) and \(A: \mathbb{R}^N\to\mathbb{R}^N\) are continuous potentials and \(f: \mathbb{R}\to\mathbb{R}\) is a subcritical nonlinear term. Under a local assumption on the potential \(V\) along with variational methods, the penalization technique and the Ljusternik-Schnirelmann theory, the authors prove the multiplicity and concentration of nontrivial solutions provided \(\varepsilon>0\) is sufficiently small.
reviewed by: Patrick Winkert
Mathematics Subject Classification ID: 35J10
zbMATH DE Number: 7341458
zbMATH Keywords: nonlinear magnetic Schrödinger equation
zbMATH Keywords: critical growth
zbMATH Keywords: multiplicity and concentration of solutions
MaRDI profile type: Publication
full work available at URL: s11856-021-2105-5
OpenAlex ID: W3130299540
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DOI: 10.1007/S11856-021-2105-5
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description: scientific article; zbMATH DE number 7341458