Perturbations of embedded eigenvalues for the bilaplacian on a cylinder

Pages: 801 - 821, Volume 21, Issue 3, July 2008

doi:10.3934/dcds.2008.21.801       Abstract        Full Text (255.6K)       Related Articles

Gianne Derks - Department of Mathematics, University of Surrey, Guildford, GU2 7XH, United Kingdom (email)
Sara Maad - Department of Mathematics, Stockholm University, SE-106 91 Stockholm, Sweden (email)
Björn Sandstede - 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.

Keywords:  embedded eigenvalue, continuous spectrum, finite multiplicity, Lyapunov--Schmidt reduction.
Mathematics Subject Classification:  Primary: 35P05, 37L05, 47A55, 47A11.

Received: June 2007;      Revised: January 2008;      Published: April 2008.