A spectral theory for a λ-rational Sturm-Liouville problem

V. Adamjan, Heinz Langer, M. Langer

Research output: Contribution to journalArticlepeer-review

20 Citations (Scopus)


We consider the regular Sturm-Liouville problem y″−py+(λ+q/(u−λ)) y=0, which contains the eigenvalue parameter rationally. Under certain assumptions on p, q, and u it is shown that the spectrum of the problem consists of a continuous component (the range of the function u), discrete eigenvalues, and possibly a finite number of embedded eigenvalues. In the considered situation the continuous spectrum is absolutely continuous, and explicit formulas for the spectral density and the corresponding Fourier transform are given.
Original languageEnglish
Pages (from-to)315-345
Number of pages31
JournalJournal of Differential Equations
Issue number2
Publication statusPublished - Feb 2001


  • nonlinear eigenvalue problem
  • spectral density
  • block operator matrix
  • numerical mathematics
  • differential equations


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