Eigenvalues below the essential spectra of singular elliptic operators

Evans, W. D.; Lewis, Roger T.

doi:10.1090/S0002-9947-1986-0849475-1

Eigenvalues below the essential spectra of singular elliptic operators
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by W. D. Evans and Roger T. Lewis PDF

Trans. Amer. Math. Soc. 297 (1986), 197-222 Request permission

Abstract:

A new technique is developed for determining if the number of eigenvalues below the essential spectrum of a singular elliptic differential operator is finite. A method is given for establishing lower bounds for the least point of the essential spectrum in terms of the behavior of the coefficients and weight near the singularities. Higher-order operators are included in these results as well as second-order Schrödinger operators.

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