Positive and oscillatory radial solutions of semilinear elliptic equations
type: Item
instance of: scholarly article
title: Positive and oscillatory radial solutions of semilinear elliptic equations
zbMATH Open document ID: 0877.35045
DOI: 10.1155/S1048953397000105
author: Shaohua Chen
author: W. Derrick
author: Joseph A. Cima
published in: Journal of Applied Mathematics and Stochastic Analysis
publication date: 1997-11-05T00:00:00Z
full work available at URL: https://eudml.org/doc/47752
review text: The authors consider the nonlinear partial differential equation \[ \Delta u+f(u)+g(|x|,u)=0 \tag{1} \] in \(\mathbb{R}^n\), \(n\geq 3\), where \(u(0)>0\), \(f\) and \(g\) are continuous, \(f(u)>0\) and \(g(|x|,u)>0\) for \(u>0\). Under some assumptions on \(f\) and \(g\) including mild conditions on the order of the growth of \(f(u)\) to zero as \(u\to 0\), they prove the nonexistence of positive or eventually positive radial solutions to the equation (1) with \(u(0)>0\).
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 34C15
zbMATH DE Number: 1023073
zbMATH Keywords: positive radial solutions
zbMATH Keywords: nonexistence
reviewed by: Yuriy V. Rogovchenko
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1023073