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.
Global persistence of the unit eigenvectors of perturbed eigenvalue problems in Hilbert spaces: the odd multiplicity case / PIERLUIGI BENEVIERI, ALESSANDRO CALAMAI, MASSIMO FURI, MARIA PATRIZIA PERA. - In: MATHEMATICS. - ISSN 2227-7390. - STAMPA. - 9:(2021), pp. 0-0. [10.3390/math9050561]
Global persistence of the unit eigenvectors of perturbed eigenvalue problems in Hilbert spaces: the odd multiplicity case
MARIA PATRIZIA PERA
2021
Abstract
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.File | Dimensione | Formato | |
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