基于混合谱数据的不连续Sturm-Liouville逆谱问题局部可解性和稳定性

Abstract

Abstract:

This paper studies inverse spectral problems for the Sturm-Liouville operator on $(0,1)$ with the Robin boundary conditions and a discontinuity at $x=d\in(0,\frac{1}{2}]$. Suppose that the known data contains one subspectrum, the potential function on $(d,1)$ as well as partial parameters in the right boundary condition and the discontinuous conditions. The paper proves the local solvability and stability for the inverse problems of recovering the potential function on $(0,d)$ and the parameter in left boundary condition, where the known potential and the parameter in the right boundary condition are allowed to contain errors.

Key words: Sturm-Liouville operator, Discontinuity condition, Local solvability, Stability

CLC Number:

O175.7

Guo Yan, Xu Xiaochuan. Local Solvability and Stability of the Inverse Spectral Problems for the Discontinuous Sturm-Liouville Problem with the Mixed Given Data[J].Acta mathematica scientia,Series A, 2024, 44(4): 859-870.

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Local Solvability and Stability of the Inverse Spectral Problems for the Discontinuous Sturm-Liouville Problem with the Mixed Given Data

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