Fine multibubble analysis in the higher-dimensional Brezis-Nirenberg problem
type: Item
instance of: scholarly article
title: Fine multibubble analysis in the higher-dimensional Brezis-Nirenberg problem
zbMATH Open document ID: 1547.35366
author: Tobias König
author: Paul Laurain
published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire
publication date: 2024-08-13T00:00:00Z
review text: This article is concerned with the study of positive solutions to \(-\Delta u+\varepsilon V u=N(N-2)u^{\frac{N+2}{N-2}}\) in a bounded open set \(\Omega\subset\mathbb{R}^N\), \(N\geq 4\). The solutions are assumed to satisfy an homogeneous Dirichlet boundary condition while the potential \(V\in C^1(\overline{\Omega})\) is negative. The main result of the article establishes the existence of solutions exhibiting multiple concentration points. It is shown that such concentration points are isolated and the authors provide a characterization of the vector of these points as a critical point of a suitable function derived from the Green function of \(-\Delta\) on \(\Omega\).
reviewed by: Marius Ghergu
Mathematics Subject Classification ID: 35J91
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35A01
zbMATH DE Number: 7896319
zbMATH Keywords: semilinear equation with Laplacian
zbMATH Keywords: Dirichlet problem
zbMATH Keywords: existence of solutions with multiple concentration points
MaRDI profile type: Publication
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DOI: 10.4171/AIHPC/95
description: scientific article; zbMATH DE number 7896319