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Perturbations of embedded eigenvalues for the bilaplacian on a cylinder

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  • 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.
    Mathematics Subject Classification: Primary: 35P05, 37L05, 47A55, 47A11.

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