Perturbations of embedded eigenvalues for the planar bilaplacian
2011 (English)In: Journal of Functional Analysis, ISSN 0022-1236, E-ISSN 1096-0783, Vol. 260, no 2, 340-398 p.Article in journal (Refereed) Published
Operators on unbounded domains may acquire eigenvalues that are embedded in the essential spectrum. Determining the fate of these embedded eigenvalues under small perturbations of the underlying operator is a challenging task, and the persistence properties of such eigenvalues are linked intimately to the multiplicity of the essential spectrum. In this paper, we consider the planar bilaplacian with potential and show that the set of potentials for which an embedded eigenvalue persists is locally an infinite-dimensional manifold with infinite codimension in an appropriate space of potentials.
Place, publisher, year, edition, pages
2011. Vol. 260, no 2, 340-398 p.
Embedded eigenvalues, Persistence, Perturbation, Bilaplacian
Research subject Mathematics
IdentifiersURN: urn:nbn:se:su:diva-51609DOI: 10.1016/j.jfa.2010.10.001ISI: 000284249000002OAI: oai:DiVA.org:su-51609DiVA: diva2:385356
FunderEU, European Research Council, MEIF-CT-2005-024191Swedish Research Council