On the existence of positive solutions for semilinear elliptic equations with singular lower order coefficients and Dirichlet boundary conditions
type: Item
instance of: scholarly article
title: On the existence of positive solutions for semilinear elliptic equations with singular lower order coefficients and Dirichlet boundary conditions
zbMATH Open document ID: 0942.35082
author: Zhen-Qing Chen
author: R. J. Williams
author: Z. Zhao
published in: Mathematische Annalen
publication date: 2000-01-31T00:00:00Z
review text: The authors give sufficient conditions which guarantee the existence of at least one positive solution to the Dirichlet problem for the semilinear elliptic equation in \(D\subset\mathbb{R}^n\), \(n\geq 3\), where \(D\) satisfies an exterior cone condition. The principal part of this equation is the Laplacian, and the minor terms are singular in the Kato class, which is, roughly speaking, \(L^p(\mathbb{R}^n)\) for \(p>{n\over 2}\). This type of equations is used to model steady-state diffusion-convection-reaction processes. An appropriate linear elliptic problem is considered that by means of implicit probabilistic representation supplies necessary a priori estimates which are exploited to apply the Schauder fixed point theorem.
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 60J65
zbMATH DE Number: 1395783
zbMATH Keywords: positive solutions
zbMATH Keywords: diffusion-convection-reaction systems
zbMATH Keywords: Schauder fixed point theorem
MaRDI profile type: Publication
full work available at URL: s002080050334
OpenAlex ID: W1976724018
DOI: 10.1007/S002080050334
description: scientific article; zbMATH DE number 1395783