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Local Solvability and Stability of an Inverse Spectral Problem for Higher-Order Differential Operators

Author

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  • Natalia P. Bondarenko

    (Department of Mechanics and Mathematics, Saratov State University, Astrakhanskaya 83, Saratov 410012, Russia
    Department of Applied Mathematics and Physics, Samara National Research University, Moskovskoye Shosse 34, Samara 443086, Russia
    S.M. Nikolskii Mathematical Institute, Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya Street, Moscow 117198, Russia)

Abstract

In this paper, we, for the first time, prove the local solvability and stability of an inverse spectral problem for higher-order ( n > 3 ) differential operators with distribution coefficients. The inverse problem consists of the recovery of differential equation coefficients from ( n − 1 ) spectra and the corresponding weight numbers. The proof method is constructive. It is based on the reduction of the nonlinear inverse problem to a linear equation in the Banach space of bounded infinite sequences. We prove that, under a small perturbation of the spectral data, the main equation remains uniquely solvable. Furthermore, we estimate the differences of the coefficients in the corresponding functional spaces.

Suggested Citation

  • Natalia P. Bondarenko, 2023. "Local Solvability and Stability of an Inverse Spectral Problem for Higher-Order Differential Operators," Mathematics, MDPI, vol. 11(18), pages 1-22, September.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:18:p:3818-:d:1233571
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    References listed on IDEAS

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    1. Natalia P. Bondarenko, 2023. "Regularization and Inverse Spectral Problems for Differential Operators with Distribution Coefficients," Mathematics, MDPI, vol. 11(16), pages 1-23, August.
    2. Natalia P. Bondarenko, 2022. "Reconstruction of Higher-Order Differential Operators by Their Spectral Data," Mathematics, MDPI, vol. 10(20), pages 1-32, October.
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    Cited by:

    1. Natalia P. Bondarenko, 2023. "Necessary and Sufficient Conditions for Solvability of an Inverse Problem for Higher-Order Differential Operators," Mathematics, MDPI, vol. 12(1), pages 1-27, December.

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    1. Natalia P. Bondarenko, 2023. "Regularization and Inverse Spectral Problems for Differential Operators with Distribution Coefficients," Mathematics, MDPI, vol. 11(16), pages 1-23, August.
    2. Natalia P. Bondarenko, 2023. "Necessary and Sufficient Conditions for Solvability of an Inverse Problem for Higher-Order Differential Operators," Mathematics, MDPI, vol. 12(1), pages 1-27, December.

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