Positive singular solutions for semilinear elliptic equations with supercritical growth
type: Item
instance of: scholarly article
title: Positive singular solutions for semilinear elliptic equations with supercritical growth
zbMATH Open document ID: 0816.35026
author: Song-Sun Lin
published in: Journal of Differential Equations
publication date: 1995-07-10T00:00:00Z
review text: The main part of the paper deals with positive, singular and radially symmetric solutions of the problem \(\Delta u+ f(u)=0\). The author shows that there exists a solution \(U(r)\) tending to \(\infty\) as \(r=| x|\to 0\) if \(f(u)\in C^ 1 (\mathbb{R})\) is supercritical at \(u=+ \infty\), and further \(U(r)\) has a finite zero if \(f(u)\) is positive for \(u>0\) and satisfies a certain subcritical condition at \(u=0\). The proof is based on a Pohozaev identity and usual ODE arguments.
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 696880
zbMATH Keywords: semilinear elliptic equation
zbMATH Keywords: super- and subcritical condition
zbMATH Keywords: positive, singular and radially symmetric solutions
MaRDI profile type: Publication
full work available at URL: jdeq.1994.1140
OpenAlex ID: W1994959111
DOI: 10.1006/JDEQ.1994.1140
Recommended article: Q4455258
Recommended article: Singular solutions for semilinear elliptic equations with general supercritical growth
Recommended article: Existence of positive solutions to semilinear elliptic systems with supercritical growth
Recommended article: Positive solutions of elliptic equations involving supercritical growth
Recommended article: Positive solutions for some singular critical growth nonlinear elliptic equations
Recommended article: Positive solutions for nonlinear singular superlinear elliptic equations
Recommended article: Large positive solutions of semilinear elliptic equations with critical and supercritical growth
Recommended article: Q3837191
Recommended article: Q4439651
Recommended article: Singularities of positive supersolutions in elliptic PDEs
description: scientific article; zbMATH DE number 696880