Existence and optimal estimates of solutions for singular nonlinear Dirichlet problems
type: Item
instance of: scholarly article
title: Existence and optimal estimates of solutions for singular nonlinear Dirichlet problems
zbMATH Open document ID: 1096.35050
author: Zhijun Zhang
author: Jiangang Cheng
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2004-09-23T00:00:00Z
review text: The goal of this paper is to study the existence and asymptotic estimates of classical solutions to the model problems \[ -\Delta_xu= \kappa(x)g(u), \quad x\in\Omega, \qquad u>0, \quad\text{in }\Omega, \qquad u=0, \quad\text{on }\partial\Omega, \tag{1} \] where \(\Omega\) is a bounded domain with \(C^2\)-boundary in \(\mathbb R^N\) \((N\geq 1)\), and \(\kappa(x)\), \(g(\cdot)\) satisfies some natural assumptions, including in particular, that (2) \(\lim_{s\to+0} g(s)= +\infty\).
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 2102517
zbMATH Keywords: semilinear elliptic equations
zbMATH Keywords: Dirichlet problems
zbMATH Keywords: singularity
zbMATH Keywords: existence
zbMATH Keywords: optimal approximations
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: j.na.2004.02.025
OpenAlex ID: W2014012044
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DOI: 10.1016/J.NA.2004.02.025
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description: scientific article; zbMATH DE number 2102517