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Critical coupling constants and eigenvalue asymptotics of perturbed periodic Sturm-Liouville operators. (English) Zbl 0953.34069
Summary: Perturbations of asymptotic decay c/r 2 arise in the partial-wave analysis of rotationally symmetric partial differential operators. The author shows that for each end-point λ 0 of the spectral bands of a perturbed periodic Sturm-Liouville operator, there is a critical coupling constant c crit such that eigenvalues in the spectral gap accumulate at λ 0 if and only if c/c crit >1. The oscillation theoretic method used in the proof also yields the asymptotic distribution of the eigenvalues near λ 0 .

MSC:
34L20Asymptotic distribution of eigenvalues for OD operators
34B24Sturm-Liouville theory
34L40Particular ordinary differential operators