Global Persistence of the Unit Eigenvectors of Perturbed Eigenvalue Problems in Hilbert Spaces: The Odd Multiplicity Case
2021
We study the persistence of eigenvalues and eigenvectors of perturbed eigenvalue problems in Hilbert spaces. We assume that the unperturbed problem has a nontrivial kernel of odd dimension and we prove a Rabinowitz-type global continuation result. The approach is topological, based on a notion of degree for oriented Fredholm maps of index zero between real differentiable Banach manifolds.
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