On a quasilinear elliptic eigenvalue problem with constraint
type: Item
instance of: scholarly article
title: On a quasilinear elliptic eigenvalue problem with constraint
zbMATH Open document ID: 1095.35018
author: J. Chen
author: Shaowei Chen
author: Yongqing Li
published in: Science in China. Series A
publication date: 2006-02-13T00:00:00Z
review text: The authors consider a quasilinear elliptic problem with constraint in the following form \[ -\text{div}(| \nabla u| ^{p-2}\nabla u)=\mu g(x,u) \quad\text{in }\Omega, \quad u=0\text{ on }\partial \Omega, \quad\int_{\Omega }| \nabla u| ^{p}\,dx=r^{p},\tag{1} \] where \(r>0,\) \(\Omega \) \(\subset \mathbb{R}^{N}\) is a bounded domain with smooth boundary \(\partial \Omega ,\) \(1<p<N.\) They construct a pseudogradient vector field \(V\) and they show the regularity of the flow associated to \(V\). By the descending flow argument, the authors prove the existence of a positive, a negative and a sign-changing solutions to problem (1).
reviewed by: Mohammed Bouchekif
Mathematics Subject Classification ID: 35P30
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 58E05
zbMATH DE Number: 5005684
zbMATH Keywords: multiple solutions
zbMATH Keywords: sign-changing solutions
zbMATH Keywords: critical point theory
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5005684