Variational principles for eigenvalues of block operator matrices

H. Langer, M. Langer, Christiane Tretter

Research output: Contribution to journalArticlepeer-review

18 Citations (Scopus)


In this paper variational principles for block operator matrices are established which are based on functionals associated with the quadratic numerical range. These principles allow to characterize, e.g., eigenvalues in gaps of the essential spectrum and to derive two-sided eigenvalue estimates in terms of the spectral characteristics of the entries of the block operator matrix. The results are applied to a second order partial differential equation depending on the spectral parameter nonlinearly.
Original languageEnglish
Pages (from-to)1427-1460
Number of pages34
JournalIndiana University Mathematics Journal
Issue number6
Publication statusPublished - 2002


  • Eigenvalues
  • block operator matrix


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