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Inverse problem for dirac system with singularities in interior points

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Abstract

We study the non-selfadjoint Dirac system on a finite interval having non-integrable regular singularities in interior points with additional matching conditions at these points. Properties of spectral characteristics are established, and the inverse spectral problem is investigated. We provide a constructive procedure for the solution of the inverse problem, and prove its uniqueness. Moreover, necessary and sufficient conditions for the global solvability of this nonlinear inverse problem are obtained.

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Acknowledgments

This work was supported by Grant 1.1436.2014K of the Russian Ministry of Education and Science and by Grant 13-01-00134 of Russian Foundation for Basic Research.

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Authors and Affiliations

  1. Department of Mathematics, Saratov State University, Astrakhanskaya 83, Saratov, 410012, Russia

    Oleg Gorbunov & Viacheslav Yurko

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  1. Oleg Gorbunov
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  2. Viacheslav Yurko
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Correspondence to Viacheslav Yurko.

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Gorbunov, O., Yurko, V. Inverse problem for dirac system with singularities in interior points. Anal.Math.Phys. 6, 1–29 (2016). https://doi.org/10.1007/s13324-015-0097-1

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  • DOI: https://doi.org/10.1007/s13324-015-0097-1

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