Eigenvalue Accumulation for Singular Sturm–Liouville Problems Nonlinear in the Spectral Parameter

For certain singular Sturm–Liouville equations whose coefficients depend continuously on the spectral parameter λ in an interval Λ it is shown that accumulation/nonaccumulation of eigenvalues at an endpoint ν of Λ is essentially determined by oscillatory properties of the equation at the boundary λ=...

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Bibliographic Details
Published in:Journal of Differential Equations 1999-12, Vol.159 (2), p.515-542
Main Author: Lutgen, Joseph P.
Format: Article
Language:English
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Summary:For certain singular Sturm–Liouville equations whose coefficients depend continuously on the spectral parameter λ in an interval Λ it is shown that accumulation/nonaccumulation of eigenvalues at an endpoint ν of Λ is essentially determined by oscillatory properties of the equation at the boundary λ=ν. As applications new results are obtained for the radial Dirac operator and the Klein–Gordon equation. Three other physical applications are also considered.
ISSN:0022-0396
1090-2732
DOI:10.1006/jdeq.1999.3671