Positive entire solutions of the equation \(\Delta{}u+f(x,u)=0\)
type: Item
instance of: scholarly article
title: Positive entire solutions of the equation \(\Delta{}u+f(x,u)=0\)
zbMATH Open document ID: 0754.35017
DOI: 10.1016/0022-0396(92)90023-G
author: Changfeng Gui
published in: Journal of Differential Equations
publication date: 1993-01-16T00:00:00Z
review text: The author considers equations of the form \(\Delta u+K(x)u^ p=0\), \(x\in R^ n\), \(n>2\), where \(\Delta\) is the \(n\)-dimensional Laplacian and \(p=(n+2)/(n-2)\). He gives and proves conditions for there to be infinitely many positive entire solutions without any pair of them intersecting and develops an asymptotic approximation to \(u(x)\) for \(| x|\) large. He uses these theorems to obtain bounds and asymptotic relations for the solutions of equations of the form \(\Delta u+f(x,u)=0\). He also points out a possible application to Riemannian geometry.
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35J99
zbMATH DE Number: 93317
zbMATH Keywords: applications to Riemannian geometry
reviewed by: Ll. G. Chambers
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 93317