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Seifert, Christian (2016): On Eigenvalue Bounds for a General Class of Sturm-Liouville Operators. In: Mathematical Physics Analysis and Geometry, Vol. 19, No. 4, 25

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We consider Sturm-Liouville operators with measure-valued weight and potential, and positive, bounded diffusion coefficient which is bounded away from zero. By means of a local periodicity condition, which can be seen as a quantitative Gordon condition, we prove a bound on eigenvalues for the corresponding operator in L-P, for 1 <= p < infinity. We also explain the sharpness of our quantitative bound, and provide an example for quasiperiodic operators.

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