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The inverse problem for differential pencils on a star-shaped graph with mixed spectral data

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Abstract

The partial inverse problem for differential pencils on a star-shaped graph is studied from mixed spectral data. More precisely, we show that if the potentials on all edges on the star-shaped graph but one are known a priori then the unknown potential on the remaining edge can be uniquely determined by partial information on the potential and a part of eigenvalues.

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Acknowledgements

The second author was supported by the Russian Ministry of Education and Science (Grant No. 1.1660.2017/4.6). The authors thank the referees for their constructive and helpful comments, which helped to improve the readability and quality of the paper.

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Authors and Affiliations

  1. Department of Applied Mathematics, Nanjing Forestry University, Nanjing, 210037, China

    Yu Ping Wang

  2. Department of Applied Mathematics and Physics, Samara National Research University, Samara, 443086, Russia

    Natalia Bondarenko

  3. Department of Mathematics, Tamkang University, New Taipei City, 25137, China

    Chung Tsun Shieh

Authors
  1. Yu Ping Wang
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  2. Natalia Bondarenko
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  3. Chung Tsun Shieh
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Correspondence to Yu Ping Wang.

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Wang, Y.P., Bondarenko, N. & Shieh, C.T. The inverse problem for differential pencils on a star-shaped graph with mixed spectral data. Sci. China Math. 63, 1559–1570 (2020). https://doi.org/10.1007/s11425-018-9485-3

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  • DOI: https://doi.org/10.1007/s11425-018-9485-3

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