Local solvability and stability of the inverse problem for the non-self-adjoint Sturm–Liouville operator

Bondarenko, Natalia P.

doi:10.1186/s13661-020-01422-4

Cited by 8 publications

(7 citation statements)

References 20 publications

(26 reference statements)

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“…where C depends only on q. In 2020, Bondarenko [14] studied the local solvability and stability for the non-self-adjoint inverse Sturm-Liouville problems with the both Robin or both Dirichlet boundary conditions by using the method of spectral mappings. The results of Borg have also been generalized into many other problems, such as the transmission eigenvalue problems [15,16], the discontinuous problems [17,18], the problems with non-separated boundary conditions [19,20], and other problems [6,[21][22][23].…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Weak and strong stability of the inverse Sturm‐Liouville problem

Guo

et al. 2023

Math Methods in App Sciences

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In this work, we study the stability of the inverse Sturm‐Liouville problem with the Neumann boundary condition at the left ending point and the Robin boundary condition at the right ending point. We estimate the difference of two potentials in the sense of weakness and ‐norm, in terms of the difference of two spectra. Since the Neumann boundary condition may become the Robin boundary condition after small perturbation of the spectra, our stability results also include this situation.

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Section: Introduction and Main Resultsmentioning

confidence: 99%

Weak and strong stability of the inverse Sturm‐Liouville problem

Guo

et al. 2023

Math Methods in App Sciences

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“…Inverse Problem 2.2. Given the data {z n , M n } ∞ n=0 , find q and h. In [2], Bondarenko proved the local solvability and stability for the above Inverse Problem 2.2. Proposition 2.2.…”

Section: Inverse Problem By the Cauchy Datamentioning

confidence: 99%

Local solvability and stability of the generalized inverse Robin-Regge problem with complex coefficients

Xu¹,

Bondarenko²

2021

Preprint

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“…For dealing with multiple eigenvalues, we use some ideas previously developed for the non-self-adjoint Sturm-Liouville operators in [37][38][39].…”

Section: Introductionmentioning

confidence: 99%

Solvability and Stability of the Inverse Problem for the Quadratic Differential Pencil

Bondarenko

Gaidel

2021

Mathematics

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The inverse spectral problem for the second-order differential pencil with quadratic dependence on the spectral parameter is studied. We obtain sufficient conditions for the global solvability of the inverse problem, prove its local solvability and stability. The problem is considered in the general case of complex-valued pencil coefficients and arbitrary eigenvalue multiplicities. Studying local solvability and stability, we take the possible splitting of multiple eigenvalues under a small perturbation of the spectrum into account. Our approach is constructive. It is based on the reduction of the non-linear inverse problem to a linear equation in the Banach space of infinite sequences. The theoretical results are illustrated by numerical examples.

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Local solvability and stability of the inverse problem for the non-self-adjoint Sturm–Liouville operator

Cited by 8 publications

References 20 publications

Weak and strong stability of the inverse Sturm‐Liouville problem

Weak and strong stability of the inverse Sturm‐Liouville problem

Local solvability and stability of the generalized inverse Robin-Regge problem with complex coefficients

Solvability and Stability of the Inverse Problem for the Quadratic Differential Pencil

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