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=ν. As applications new results are obtained for the radial Dirac operator and the Klein–Gordon equation. Three other physical applications are also considered.