Positive solutions for semilinear elliptic equations with critical weighted Hardy-Sobolev exponents
type: Item
instance of: scholarly article
title: Positive solutions for semilinear elliptic equations with critical weighted Hardy-Sobolev exponents
zbMATH Open document ID: 1341.35032
author: Haiyan Liu
author: Chun-Lei Tang
published in: Bulletin of the Belgian Mathematical Society - Simon Stevin
publication date: 2016-02-03T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.bbms/1447856063
review text: In this paper, the following semilinear elliptic problem \[ \begin{cases} -\operatorname{div}(|x|^{-2a}\nabla u)-\mu\frac{u}{|x|^{2(1+a)}}=\frac{|u|^{p-2}}{|x|^{bp}}u+f(x,u),\quad & x\in\Omega, \\ u= 0,\quad & x\in\partial\Omega\end{cases} \] is considered, where \(\Omega\subset\mathbb R^N\) is a bounded domain with smooth boundary \(\partial \Omega\), \(N\geq 3\), \(0\in\Omega\), \(0\leq a<\sqrt{\overline{\mu}}\), \(0\leq\mu<(\sqrt{\overline{\mu}}-a)^2\) with \(\overline{\mu}=(N-2)^2/4\), \(a\leq b<a+1\), and \(p=2N/(N-2(1+a-b))\) is the Hardy-Sobolev critical exponent. The existence result of positive solutions is established.
reviewed by: Satoshi Tanaka
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35J20
Mathematics Subject Classification ID: 35J61
Mathematics Subject Classification ID: 35J75
Mathematics Subject Classification ID: 35B33
Mathematics Subject Classification ID: 35B09
zbMATH DE Number: 6538893
zbMATH Keywords: weighted Hardy-Sobolev exponents
zbMATH Keywords: mountain pass lemma
zbMATH Keywords: semilinear elliptic equation
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 6538893