Positive constrained minimizers for supercritical problems in the ball
type: Item
instance of: scholarly article
title: Positive constrained minimizers for supercritical problems in the ball
zbMATH Open document ID: 1261.35052
DOI: 10.1090/S0002-9939-2011-11133-X
author: Massimo Grossi
author: Benedetta Noris
published in: Proceedings of the American Mathematical Society
publication date: 2012-05-29T00:00:00Z
full work available at URL: https://arxiv.org/abs/1006.5360
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35B09
zbMATH DE Number: 6038845
MaRDI profile type: Publication
arXiv ID: 1006.5360
cites work: Q4863664
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review text: This paper studies the existence of radial solutions to the equation \(\Delta u+V(| x|)u=u^p\) in the unit ball of \(\mathbb R^n\), \(n\geq 2\). The authors provide a sufficient condition for the existence of a positive solution to the equation above, when \(p\) is large enough both with Neumann and Dirichlet homogeneous boundary conditions. The solution turns out to be a constrained minimum of the associated energy functional. As an application, they show that the Neumann problem always admits a solution if \(V(| x|)\geq 0\), \(V\not\equiv 0\) is smooth and \(p\) is sufficiently large.
reviewed by: Riikka Korte
description: scientific article; zbMATH DE number 6038845