Inverse spectral problems for the Sturm-Liouville operator with discontinuity

Xiao-Chuan Xu; Chuan-Fu Yang

doi:10.1016/j.jde.2016.11.024

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arXiv · 1703.01403

Inverse spectral problems for the Sturm-Liouville operator with discontinuity

Xiao-Chuan Xu·Chuan-Fu Yang

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Abstract

In this work, we consider the Sturm-Liouville operator on a finite interval $[0,1]$ with discontinuous conditions at $1/2$. We prove that if the potential is known a priori on a subinterval $[b,1]$ with $b\ge1/2$, then parts of two spectra can uniquely determine the potential and all parameters in discontinuous conditions and boundary conditions. For the case $b<1/2$, parts of either one or two spectra can uniquely determine the potential and a part of parameters.

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BibTeX RIS

Xiao-Chuan Xu, Chuan-Fu Yang. 2017-03-04. Inverse spectral problems for the Sturm-Liouville operator with discontinuity. https://doi.org/10.1016/j.jde.2016.11.024

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