Perturbations of embedded eigenvalues for the bilaplacian on a cylinder
Gianne Derks - Department of Mathematics, University of Surrey, Guildford, GU2 7XH, United Kingdom (email)
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.
eigenvalue, continuous spectrum, finite multiplicity,
Received: June 2007; Revised: January 2008; Published: April 2008.
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