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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.
Please use this url to cite or link to this publication:
author
; and
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
2025-10-14 09:43:01
@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}},
}