Spectral and related properties about the Emden-Fowler equation \(-\Delta u=\lambda e^ u\) on circular domains
type: Item
instance of: scholarly article
title: Spectral and related properties about the Emden-Fowler equation \(-\Delta u=\lambda e^ u\) on circular domains
zbMATH Open document ID: 0799.35086
DOI: 10.1007/BF01459770
author: Ken'ichi Nagasaki
author: Takashi Suzuki
published in: Mathematische Annalen
publication date: 1994-06-15T00:00:00Z
full work available at URL: https://eudml.org/doc/165196
review text: The Emden-Fowler equation with Dirichlet boundary conditions is investigated. The domain is assumed to be the unit ball or an annulus in \(\mathbb{R}^ n\) with \(2<n<10\). The authors study the behaviour of radially symmetric solutions for varying values of \(\lambda\) and the annulus' inner radius. The linearized problem in radial direction is solved using the Emden transformation yielding an autonomous nonlinear ordinary differential equation, which can be investigated by phase plane analysis. Also the occurrence of nonradial bifurcations in the annular case is treated.
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 35P30
Mathematics Subject Classification ID: 35B32
zbMATH DE Number: 590000
zbMATH Keywords: Emden-Fowler equation
zbMATH Keywords: Dirichlet boundary conditions
zbMATH Keywords: radially symmetric solutions
zbMATH Keywords: phase plane analysis
zbMATH Keywords: nonradial bifurcations
reviewed by: Alois Steindl
MaRDI profile type: Publication
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OpenAlex ID: W1972671559
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description: scientific article; zbMATH DE number 590000