On non-radially symmetric bifurcation in the annulus
type: Item
instance of: scholarly article
title: On non-radially symmetric bifurcation in the annulus
zbMATH Open document ID: 0688.35005
DOI: 10.1016/0022-0396(89)90084-3
author: Song-Sun Lin
published in: Journal of Differential Equations
publication date: 1989-01-01T00:00:00Z
review text: The author considers the equation \(-\Delta u=\lambda e^ u\) on a two- dimensional annulus with Dirichlet boundary conditions. He explicitly finds the radially symmetric solutions and finds the points where non radially symmetric solutions bifurcate from symmetric ones. Reviewer's remark: More recently the reviewer has used the degree in his paper [Ann. Inst. Henri Poincaré, Anal. Nonlineaire 2, 329-370 (1985; Zbl 0579.58022)] to prove that there is a non-radially symmetric solution for each \(\lambda\) in \((0,\lambda^*)\) where \(\lambda^*\) is the largest point of non radially symmetric bifurcation. In fact, there is an unbounded continua of non-radially symmetric solutions.
Mathematics Subject Classification ID: 35B32
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 47J05
Mathematics Subject Classification ID: 35P30
zbMATH DE Number: 4127679
zbMATH Keywords: breaking of symmetry
zbMATH Keywords: radially symmetric solutions
zbMATH Keywords: degree
reviewed by: E. N. Dancer
MaRDI profile type: Publication
full work available at URL: 0022-0396(89)90084-3
OpenAlex ID: W1973559315
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description: scientific article; zbMATH DE number 4127679