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Perturbations of embedded eigenvalues for the bilaplacian on a cylinder

Derks, Gianne; Maad, Sara LU and Sandstede, Björn (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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author
publishing date
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
2017-05-02 10:49:03
@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},
  keyword      = {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},
  volume       = {21},
  year         = {2008},
}