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2008, 21(3): 801-821. doi: 10.3934/dcds.2008.21.801

Perturbations of embedded eigenvalues for the bilaplacian on a cylinder

1. 

Department of Mathematics, University of Surrey, Guildford, GU2 7XH, United Kingdom

2. 

Department of Mathematics, Stockholm University, SE-106 91 Stockholm, Sweden

Received  June 2007 Revised  January 2008 Published  April 2008

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.
Citation: Gianne Derks, Sara Maad, Björn Sandstede. Perturbations of embedded eigenvalues for the bilaplacian on a cylinder. Discrete & Continuous Dynamical Systems - A, 2008, 21 (3) : 801-821. doi: 10.3934/dcds.2008.21.801
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