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The Spectral Properties of a Two-Term Fourth-Order Operator with a Spectral Parameter in the Boundary Condition

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Abstract

We consider a spectral problem for a two-term fourth-order differential operator with nonsmooth potential. The boundary conditions involve a spectral parameter. We obtain eigenvalue asymptotics at high energy and a regularized trace formula for this operator.

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Authors and Affiliations

  1. Southern Mathematical Institute, Vladikavkaz Scientific Center of the Russian Academy of Sciences, Vladikavkaz, Russia

    D. M. Polyakov

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  1. D. M. Polyakov
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Correspondence to D. M. Polyakov.

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Translated from Sibirskii Matematicheskii Zhurnal, 2023, Vol. 64, No. 3, pp. 611–634. https://doi.org/10.33048/smzh.2023.64.313

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Polyakov, D.M. The Spectral Properties of a Two-Term Fourth-Order Operator with a Spectral Parameter in the Boundary Condition. Sib Math J 64, 649–669 (2023). https://doi.org/10.1134/S0037446623030138

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  • DOI: https://doi.org/10.1134/S0037446623030138

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