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An inverse problem for an integro-differential pencil with polynomial eigenparameter-dependence in the boundary condition

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Abstract

The boundary value problem for the first-order integro-differential equation is considered with the periodic boundary condition, polynomially dependent on the spectral parameter. The inverse problem is studied, which consists in reconstruction of the convolution kernel and the polynomial in the boundary condition, by using the spectrum. We obtain (1) uniqueness, (2) a constructive procedure for solution, (3) necessary and sufficient conditions for solvability of the inverse problem.

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Acknowledgements

This work was supported by Grant 17-11-01193 of the Russian Science Foundation.

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Authors and Affiliations

  1. Department of Applied Mathematics and Physics, Samara National Research University, Moskovskoye Shosse 34, Samara, Russia, 443086

    Natalia P. Bondarenko

  2. Department of Mechanics and Mathematics, Saratov State University, Astrakhanskaya 83, Saratov, Russia, 410012

    Natalia P. Bondarenko

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  1. Natalia P. Bondarenko
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Correspondence to Natalia P. Bondarenko.

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Bondarenko, N.P. An inverse problem for an integro-differential pencil with polynomial eigenparameter-dependence in the boundary condition. Anal.Math.Phys. 9, 2227–2236 (2019). https://doi.org/10.1007/s13324-019-00332-8

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  • DOI: https://doi.org/10.1007/s13324-019-00332-8

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