On Rabinowitz alternative for the Laplace-Beltrami operator on \(S^{n-1}\)
type: Item
instance of: scholarly article
title: On Rabinowitz alternative for the Laplace-Beltrami operator on \(S^{n-1}\)
zbMATH Open document ID: 0879.35020
published in: Differential and Integral Equations
publication date: 1997-12-10T00:00:00Z
review text: New versions of the Rabinowitz alternative theorem for \(S^1\)-equivariant gradient maps are given. The structure of eigenspaces of the Laplace-Beltrami operator on \(S^{n-1}\) is described. It is proved that any continuum of nontrivial solutions of the equation \(-\Lambda u = f(\lambda ,u)\) (where \(\Lambda\) is the Laplace-Beltrami operator on \(S^{n-1}\)) is unbounded in \(H^1(S^{n-1})\times \mathbb{R}\).
Mathematics Subject Classification ID: 35B32
Mathematics Subject Classification ID: 35J20
Mathematics Subject Classification ID: 35P30
zbMATH DE Number: 1095812
zbMATH Keywords: Laplace-Beltrami operator on \(S^{n-1}\)
zbMATH Keywords: global bifurcation
zbMATH Keywords: Rabinowitz alternative
author: Sławomir Maciej Rybicki
reviewed by: Milan Kučera
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1095812