Perturbations of embedded eigenvalues for the bilaplacian on a cylinder
(2008) In Discrete and Continuous Dynamical Systems. Series A 21(3). p.801-821- Abstract
- Perturbation problems for operators with embedded eigenvalues are generally challenging since the embedded eigenvalues cannot be separated from the rest of the spectrum. In this paper we study a perturbation problem for embedded eigenvalues for the bilaplacian with an added potential, when the underlying domain is a cylinder. We show that the set of nearby potentials, for which a simple embedded eigenvalue persists, forms a smooth manifold of finite codimension.
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https://lup.lub.lu.se/record/ba042b59-7285-4b24-be58-d71add5b43c7
- author
- Derks, Gianne ; Maad, Sara LU and Sandstede, Björn
- publishing date
- 2008
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- embedded eigenvalue, continuous spectrum, finite multiplicity, Lyapunov-Schmidt reduction
- in
- Discrete and Continuous Dynamical Systems. Series A
- volume
- 21
- issue
- 3
- pages
- 21 pages
- publisher
- American Institute of Mathematical Sciences
- external identifiers
-
- scopus:45849085790
- ISSN
- 1078-0947
- DOI
- 10.3934/dcds.2008.21.801
- language
- English
- LU publication?
- no
- id
- ba042b59-7285-4b24-be58-d71add5b43c7
- date added to LUP
- 2017-02-08 13:48:37
- date last changed
- 2022-04-16 23:14:20
@article{ba042b59-7285-4b24-be58-d71add5b43c7, abstract = {{Perturbation problems for operators with embedded eigenvalues are generally challenging since the embedded eigenvalues cannot be separated from the rest of the spectrum. In this paper we study a perturbation problem for embedded eigenvalues for the bilaplacian with an added potential, when the underlying domain is a cylinder. We show that the set of nearby potentials, for which a simple embedded eigenvalue persists, forms a smooth manifold of finite codimension.}}, author = {{Derks, Gianne and Maad, Sara and Sandstede, Björn}}, issn = {{1078-0947}}, keywords = {{embedded eigenvalue; continuous spectrum; finite multiplicity; Lyapunov-Schmidt reduction}}, language = {{eng}}, number = {{3}}, pages = {{801--821}}, publisher = {{American Institute of Mathematical Sciences}}, series = {{Discrete and Continuous Dynamical Systems. Series A}}, title = {{Perturbations of embedded eigenvalues for the bilaplacian on a cylinder}}, url = {{http://dx.doi.org/10.3934/dcds.2008.21.801}}, doi = {{10.3934/dcds.2008.21.801}}, volume = {{21}}, year = {{2008}}, }