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A class of higher order inverse spectral problems

Acta Mathematica Sinica,English Series 2024年

作者： Ai Wei GUAN Chuan Fu YANG natalia P.bondarenko Department of Mathematics School of Mathematics and Statistics Nanjing University of Science and Technology S.M. Nikolskii Mathematical Institute Peoples’ Friendship University of Russia (RUDN University) Moscow Center of Fundamental and Applied Mathematics Lomonosov Moscow State University

In this paper, we consider the recovery of third-order differential operators from two spectra, as well as fourth-order or fifth-order differential operators from three spectra, where these differential operators are endowed with complex-valued distributional coefficients. For the case of multiple spectra, we first establish the relationship between spectra and the Weyl-Yurko matrix. Secondly, we prove the uniqueness theorem for the solution of the inverse problems. Our approach allows us to obtain results for the general case of complex-valued distributional coefficients.

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On the Local Solvability and Stability for the Inverse Spectral Problem of the Generalized Dirichlet–Regge Problem

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Acta Mathematica Sinica,English Series 2022年第7期38卷 1229-1240页

作者： Xiao Chuan XU natalia Pavlovna bondarenko School of Mathematics and Statistics Nanjing University of Information Science and TechnologyNanjing 210044P.R.China Department of Applied Mathematics and Physics Samara National Research UniversityMoskovskoye Shosse 34Samara 443086Russia Department of Mechanics and Mathematics Saratov State UniversityAstrakhanskaya 83Saratov 410012Russia

For the generalized Dirichlet–Regge problem with complex coefficients,we prove the local solvability and stability for the inverse spectral problem,which indicates an improved result of the previous work([Journal of ... 详细信息

关键词： Dirichlet-Regge problem inverse spectral problem local solvability stability reconstruction algorithm

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The inverse problem for differential pencils on a star-shaped graph with mixed spectral data

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Science China Mathematics 2020年第8期63卷 1559-1570页

作者： Yu Ping Wang natalia bondarenko Chung Tsun Shieh Department of Applied Mathematics Nanjing Forestry UniversityNanjing 210037China Department of Applied Mathematics and Physics Samara National Research UniversitySamara 443086Russia Department of Mathematics Tamkang UniversityNew Taipei City 25137China

The partial inverse problem for differential pencils on a star-shaped graph is studied from mixed spectral *** precisely,we show that if the potentials on all edges on the star-shaped graph but one are known a priori then the unknown potential on the remaining edge can be uniquely determined by partial information on the potential and a part of eigenvalues.

关键词： inverse spectral problem differential pencils potential star-shaped graph

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