<p>This paper addresses the uniqueness of the solution to the inverse problem for a Dirac-type functional–differential operator with two constant delays. It is known that the solution is unique when both delays are at least two-fifths of the interval length and that it is not unique when they are smaller. Additionally, the inverse problem is solved if the first delay is not less than one-third of the interval length. The issue of establishing uniqueness for arbitrary delays has been very challenging. In this study, we provide a comprehensive solution to this problem, offering a complete analysis of the inverse problem for any pair of two constant delays.</p>

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On non-uniqueness of recovering Dirac operators with two constant delays

  • Biljana Vojvodić,
  • Nebojša Djurić

摘要

This paper addresses the uniqueness of the solution to the inverse problem for a Dirac-type functional–differential operator with two constant delays. It is known that the solution is unique when both delays are at least two-fifths of the interval length and that it is not unique when they are smaller. Additionally, the inverse problem is solved if the first delay is not less than one-third of the interval length. The issue of establishing uniqueness for arbitrary delays has been very challenging. In this study, we provide a comprehensive solution to this problem, offering a complete analysis of the inverse problem for any pair of two constant delays.