Abstract
We consider the Sturm–Liouville problem on the interval [0, 1] with the Dirichlet boundary conditions and a weighted integral condition on the potential function, which allows the potential to have singularities of different orders at the end-points. For some values of the parameters of the weight functions, estimates are obtained for the first eigenvalue of this problem, and a method is proposed for finding precise bounds for this eigenvalue in some cases.
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Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 32, pp. 162–190, 2019.
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Ezhak, S.S., Telnova, M.Y. Estimates for The First Eigenvalue of the Sturm–Liouville Problem with Potentials in Weighted Spaces. J Math Sci 244, 216–234 (2020). https://doi.org/10.1007/s10958-019-04615-0
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DOI: https://doi.org/10.1007/s10958-019-04615-0