Classification of positive solutions of quasilinear elliptic equations
type: Item
instance of: scholarly article
title: Classification of positive solutions of quasilinear elliptic equations
zbMATH Open document ID: 0813.35019
DOI: 10.12775/TMNA.1994.001
author: James Serrin
author: Henghui Zou
published in: Topological Methods in Nonlinear Analysis
publication date: 1995-05-29T00:00:00Z
review text: This is a very substantial and beautiful survey on the classification and properties of positive solutions of the equation \[ \Delta u + f \bigl( | x |, u, | \nabla u | \bigr) = 0 \quad \bigl( x \in \mathbb{R}^ n \backslash \{0\} \bigr), \] with a particular emphasis on the cases \(f(r,u,v) = u^ p\), \(f(r,u,v) = u^ p + u^ q\), and \(f(r,u,v) = u^ p - v^ q\). In the case \(f(r,u,v) = u^ p + v^ q\), for example, the number and behaviour of solutions depend in a very sensitive way on the range of the exponents \(p\) and \(q\) below or above the ``critical'' values \(n/(n-2)\) and \((n+2)/(n-2)\). Many illuminating examples are given.
reviewed by: Jürgen Appell
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35B05
Mathematics Subject Classification ID: 35A05
zbMATH DE Number: 640267
zbMATH Keywords: classification and properties of positive solutions
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 640267