On Rabinowitz alternative for the Laplace-Beltrami operator on \(S^{n-1}\)
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 \(H^1(S^{n-1})\times \mathbb{R}\).
Laplace-Beltrami operator on \(S^{n-1}\)
scientific article; zbMATH DE number 1095812