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

Natalia P. Bondarenko ()
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Natalia P. Bondarenko: Department of Mechanics and Mathematics, Saratov State University, Astrakhanskaya 83, Saratov 410012, Russia

Mathematics, 2023, vol. 11, issue 18, 1-22

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.

Keywords: inverse spectral problem; higher-order differential operators; distribution coefficients; local solvability; stability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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