Solvability of the Neumann problem in a ball for \(-\Delta u + u^{-\nu} = h(| x |), \nu > 1\)
type: Item
instance of: scholarly article
title: Solvability of the Neumann problem in a ball for \(-\Delta u + u^{-\nu} = h(| x |), \nu > 1\)
zbMATH Open document ID: 0845.35032
published in: Journal of Differential Equations
publication date: 1996-09-11T00:00:00Z
review text: The authors obtain existence and uniqueness results for radially symmetric solutions of the elliptic problem \(- d\Delta u+ u^{- \nu}= h\) on \(B\) with zero Neumann boundary condition \((\nu> 1, d> 0)\). \(B\) is the unit ball in \(\mathbb R^N\) with \(N\geq 2\). Assuming that the (radial) function \(h\) satisfies \(\int_B h\, dx> 0\) they obtain the existence of a solution. With the additional assumption that \(d\) is sufficiently large the solution is shown to be unique. Existence of a positive solution follows for the integral being strictly positive.
reviewed by: Guido Sweers
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 838712
zbMATH Keywords: semilinear elliptic problem
zbMATH Keywords: radially symmetric solution
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
author: Manuel del Pino
author: Gaston E. Hernandez
MaRDI profile type: Publication
full work available at URL: jdeq.1996.0004
OpenAlex ID: W2054436582
DOI: 10.1006/JDEQ.1996.0004
description: scientific article; zbMATH DE number 838712