2020
DOI: 10.48550/arxiv.2012.10107
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The number of Dirac-weighted eigenvalues of Sturm-Liouville equations with integrable potentials and an application to inverse problems

Xiao Chen,
Jiangang Qi

Abstract: In this paper, we further Meirong Zhang, et al.'s work by computing the number of weighted eigenvalues for Sturm-Liouville equations, equipped with general integrable potentials and Dirac weights, under Dirichlet boundary condition. We show that, for a Sturm-Liouville equation with a general integrable potential, if its weight is a positive linear combination of n Dirac Delta functions, then it has at most n (may be less than n, or even be 0) distinct real Dirichlet eigenvalues, or every complex number is a Di… Show more

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