Standing waves for nonlinear Schrödinger equations involving critical growth of Trudinger-Moser type
type: Item
instance of: scholarly article
title: Standing waves for nonlinear Schrödinger equations involving critical growth of Trudinger-Moser type
zbMATH Open document ID: 1334.35328
author: Jianjun Zhang
author: João Marcos do Ó
published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik
publication date: 2016-01-05T00:00:00Z
review text: From the abstract: In this paper, we deal with the following singularly perturbed elliptic problem \[ -\varepsilon^2 \Delta u+V(x) u=f(u), \quad u \in H^1(\mathbb{R}^2), \] where \(f(s)\) has critical growth of Trudinger-Moser type. In this paper, we construct a localized bound-state solution concentrating at an isolated component of the positive local minimum points of \(V\) as \(\varepsilon \rightarrow 0\) under certain conditions on \(f(s)\). Our results complete the analysis made in [\textit{J. Byeon} et al., Commun. Partial Differ. Equations 33, No. 6, 1113--1136 (2008; Zbl 1155.35344)] for the two-dimensional case, in the sense that, in that paper only the subcritical growth was considered.
reviewed by: Alessandro Selvitella
Mathematics Subject Classification ID: 35Q55
Mathematics Subject Classification ID: 35B25
Mathematics Subject Classification ID: 35B33
Mathematics Subject Classification ID: 35J61
zbMATH DE Number: 6526482
zbMATH Keywords: nonlinear Schrödinger equations
zbMATH Keywords: standing waves
zbMATH Keywords: variational methods
zbMATH Keywords: critical growth
zbMATH Keywords: Trudinger-Moser inequalities
zbMATH Keywords: lack of compactness
zbMATH Keywords: unbounded domains
MaRDI profile type: Publication
full work available at URL: s00033-015-0565-3
OpenAlex ID: W1234013517
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DOI: 10.1007/S00033-015-0565-3
description: scientific article; zbMATH DE number 6526482