Asymptotic behavior of the solution for an elliptic boundary value problem with exponential nonlinearity
type: Item
instance of: scholarly article
title: Asymptotic behavior of the solution for an elliptic boundary value problem with exponential nonlinearity
zbMATH Open document ID: 0709.35042
author: Takashi Suzuki
author: Ken'ichi Nagasaki
published in: Proceedings of the Japan Academy. Series A
publication date: 1989-01-01T00:00:00Z
review text: The branch of large solutions of the problem \(\Delta u+\lambda e^ u=0\) in \(D\subset {\mathbb{R}}^ n\), \(u=0\) on \(\partial D\) is discussed when \(\lambda\to 0\). The location of the singularities is determined and it depends on the Green's function. The proof uses some a priori bounds for the solutions and a representation formula which is due to Liouville.
reviewed by: Catherine Bandle
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 35P30
Mathematics Subject Classification ID: 35B30
zbMATH DE Number: 4165462
zbMATH Keywords: exponential nonlinearity
zbMATH Keywords: singularities
zbMATH Keywords: Green's function
MaRDI profile type: Publication
full work available at URL: pjaa.65.74
OpenAlex ID: W2074268955
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DOI: 10.3792/PJAA.65.74
description: scientific article; zbMATH DE number 4165462