Inverse Sturm–Liouville problems with the potential known on an interior subinterval

Abstract

The uniqueness problem of inverse Sturm–Liouville problems with the potential known on an interior subinterval is considered. We prove that the potential on the entire interval and boundary conditions are uniquely determined in terms of the known eigenvalues and some information on the eigenfunctions at some interior point (interior spectral data). Moreover, we also concern with the situation where the potential q is C^2k-smoothness at some given points.

Keywords:

• eigenvalue
• interior spectral data
• inverse spectral problem

AMS Subject Classifications:

• Primary 34L05
• 34A55
• Secondary 34L40

Acknowledgements

The authors would like to thank the referee for careful reading of the manuscript and helping us to improve the presentation of this paper.

Notes

1 The research was supported in part by the NNSF (No.11171198) and Fundamental Research Funds for the Central Universities (No. GK 201304001) of China.