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Partial Inverse Problems for the Sturm–Liouville Operator on a Star-Shaped Graph with Different Edge Lengths

  • Natalia Pavlovna Bondarenko
  • Chuan-Fu Yang
Article

Abstract

The Sturm–Liouville operator with singular potentials from the class \(W_2^{-1}\) is considered on a star-shaped graph with different edge lengths. We suppose that the potentials are known a priori on a part of the edges, and study the partial inverse problems, that consist in recovering the potentials on the other edges from a fractional part of the spectrum and some additional data. We prove three uniqueness theorems and provide a constructive algorithm for the solution of the inverse problems.

Keywords

Partial inverse spectral problem Sturm–Liouville operator quantum graph singular potential 

Mathematics Subject Classification

34A55 34B05 34B09 34B45 34L20 34L40 47E05 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Applied MathematicsNanjing University of Sciences and TechnologyNanjingChina
  2. 2.Department of Applied MathematicsSamara National Research UniversitySamaraRussia
  3. 3.Department of Mechanics and MathematicsSaratov State UniversitySaratovRussia

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