Perturbations of embedded eigenvalues for the planar bilaplacian

Research output: Contribution to journalArticle


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.


External organisations
  • University of Surrey
  • Stockholm University
  • Brown University
Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Mathematical Analysis


  • Embedded eigenvalues, Persistence, Perturbation, Bilaplacian
Original languageEnglish
Pages (from-to)340-398
Number of pages59
JournalJournal of Functional Analysis
Issue number2
Publication statusPublished - 2011
Publication categoryResearch