Perturbations of embedded eigenvalues for the bilaplacian on a cylinder
Gianne Derks, Sara Maad, Björn Sandstede · Discrete and Continuous Dynamical Systems · 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.