On the local solvability and stability of the partial inverse problems for the non-self-adjoint Sturm-Liouville operators with a discontinuity

Xiao-Chuan Xu; Chuan-Fu Yang; Natalia Pavlovna Bondarenko

doi:10.1063/5.0233344

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arXiv · 2404.13261

On the local solvability and stability of the partial inverse problems for the non-self-adjoint Sturm-Liouville operators with a discontinuity

Xiao-Chuan Xu·Chuan-Fu Yang·Natalia Pavlovna Bondarenko

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Abstract

In this work, we study the inverse spectral problems for the Sturm-Liouville operators on [0,1] with complex coefficients and a discontinuity at $x=a\in(0,1)$. Assume that the potential on (a,1) and some parameters in the discontinuity and boundary conditions are given. We recover the potential on (0,a) and the other parameters from the eigenvalues. This is the so-called partial inverse problem. The local solvability and stability of the partial inverse problems are obtained for $a\in(0,1)$, in which the error caused by the given partial potential is considered. As a by-product, we also obtain two new uniqueness theorems for the partial inverse problem.

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BibTeX RIS

Xiao-Chuan Xu, Chuan-Fu Yang, Natalia Pavlovna Bondarenko. 2024-04-20. On the local solvability and stability of the partial inverse problems for the non-self-adjoint Sturm-Liouville operators with a discontinuity. https://doi.org/10.1063/5.0233344

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