Positive solutions of nonlinear elliptic singular boundary value problems in a ball.
type: Item
instance of: scholarly article
title: Positive solutions of nonlinear elliptic singular boundary value problems in a ball.
zbMATH Open document ID: 1096.35043
DOI: 10.1007/BF02935758
author: Lokenath Debnath
author: Xingye Xu
published in: Journal of Applied Mathematics and Computing
publication date: 2004-09-28T00:00:00Z
review text: The authors deal with the existence of positive solutions of the following singular nonlinear elliptic boundary value problem \[ \begin{cases} \Delta u+f(x,\nabla u)u^{-\lambda}=0,\quad & x\in B\subset\mathbb{R}^N\\ u=0,\quad & x\in\partial B,\end{cases}\tag{1} \] where \(B=\{x\in\mathbb{R}^N \mid|x|<1\}\) and \(\nabla\) denote the \(N\)-dimensional gradient operator. The main goal of the authors is to prove existence of positive solutions of (1) belonging to \(C^2(B)\cap C(\overline B)\).
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35B05
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 2103983
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
cites work: On a dirichlet problem with a singular nonlinearity
cites work: On a singular elliptic boundary value problem in a ball
cites work: Q5187597
cites work: On semilinear elliptic boundary value problems in unbounded domains
cites work: Q4073917
full work available at URL: https://doi.org/10.1007/bf02935758
OpenAlex ID: W1989241396
description: scientific article; zbMATH DE number 2103983