Regular approximation of singular third-order differential operators

Zhang, Maozhu; Li, Kun; Wang, Yicao

doi:10.1016/j.jmaa.2022.126940

Cited by 5 publications

(2 citation statements)

References 26 publications

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“…In recent years, spectral theory of the third-order differential operators with non-smooth and distributional coefficients attracts considerable attention of scholars (see, e.g., [1][2][3][4][5][6][7]). The third-order differential equations arise in various physical applications, e.g., in modelling thin membrane flow of viscous liquid and elastic beam vibrations (see [8][9][10]).…”

Section: Introductionmentioning

confidence: 99%

Inverse spectral problem for the third-order differential equation

Bondarenko¹

2023

Preprint

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This paper is concerned with the inverse spectral problem for the third-order differential equation with distribution coefficient. The inverse problem consists in the recovery of the differential expression coefficients from the spectral data of two boundary value problems with separated boundary conditions. For this inverse problem, we solve the most fundamental question of the inverse spectral theory about the necessary and sufficient conditions of solvability. In addition, we prove the local solvability and stability of the inverse problem. Furthermore, we obtain very simple sufficient conditions of solvability in the self-adjoint case. The main results are proved by a constructive method that reduces the nonlinear inverse problem to a linear equation in the Banach space of bounded infinite sequences. In the future, our results can be generalized to various classes of higher-order differential operators with integrable or distribution coefficients.

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Section: Introductionmentioning

confidence: 99%

Inverse spectral problem for the third-order differential equation

Bondarenko¹

2023

Preprint

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“…Some six-order eigenvalue problems that occur in mathematical models of vibrations of curved arches were considered in [40]. In recent years, the interest of scholars to spectral properties of the third-and the fourth-order differential operators with non-smooth and distribution coefficients has increased (see, e.g., [41][42][43][44][45]). Thus, the investigation of higher-order differential operators with distribution coefficients, on the one hand, is useful for the development of mathematical methods for a wider range of applied problems.…”

Section: Introductionmentioning

confidence: 99%

Inverse Spectral Problems for Arbitrary-Order Differential Operators with Distribution Coefficients

Bondarenko

2021

Mathematics

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In this paper, we propose an approach to inverse spectral problems for the n-th order (n≥2) ordinary differential operators with distribution coefficients. The inverse problems which consist in the reconstruction of the differential expression coefficients by the Weyl matrix and by several spectra are studied. We prove the uniqueness of solution for these inverse problems, by developing the method of spectral mappings. The results of this paper generalize the previously known results for the second-order differential operators with singular potentials and for the higher-order differential operators with regular coefficients. In the future, the approach of this paper can be used for constructive solution and for investigation of solvability of the considered inverse problems.

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Inverse Spectral Problem for the Third-Order Differential Equation

Bondarenko

2023

Results Math

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Regular approximation of singular third-order differential operators

Cited by 5 publications

References 26 publications

Inverse spectral problem for the third-order differential equation

Inverse spectral problem for the third-order differential equation

Inverse Spectral Problems for Arbitrary-Order Differential Operators with Distribution Coefficients

Inverse Spectral Problem for the Third-Order Differential Equation

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