Existence and symmetry of multi-bump solutions for nonlinear Schrödinger equations
type: Item
instance of: scholarly article
title: Existence and symmetry of multi-bump solutions for nonlinear Schrödinger equations
zbMATH Open document ID: 1005.35083
author: Zhi-Qiang Wang
published in: Journal of Differential Equations
publication date: 2003-02-14T00:00:00Z
review text: The author studies the existence and symmetry property of multi-bump solutions of the equation \(-\Delta v+\lambda V(x)v=v^p\), \(v>0\), in \(\mathbb{R}^N\). Especially when the potential \(V\) is radially symmetric, i.e., \(V(x)=V(|x|)\), multi-bump solutions are constructed with bumps concentrated on a simply-connected component of the set of global minimum points of \(V\). Furthermore, conditions are given to assure that the multi-bump solutions obtained have prescribed subgroups of \(O(N)\) as their exact symmetry. Consequently, many non-radial solutions of the equation are constructed with prescribed exact symmetry.
reviewed by: Wen-Xiu Ma
Mathematics Subject Classification ID: 35Q55
Mathematics Subject Classification ID: 35J60
zbMATH DE Number: 1389119
zbMATH Keywords: nonlinear Schrödinger equations
zbMATH Keywords: multi-bump solutions
zbMATH Keywords: existence
zbMATH Keywords: symmetry
MaRDI profile type: Publication
OpenAlex ID: W2026315402
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DOI: 10.1006/JDEQ.1999.3650
description: scientific article; zbMATH DE number 1389119