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Results in Mathematics

, 74:45 | Cite as

Inverse Spectral Problems for Sturm–Liouville Operators with a Constant Delay Less than Half the Length of the Interval and Robin Boundary Conditions

  • Milenko Pikula
  • Vladimir VladičićEmail author
  • Biljana Vojvodić
Article
  • 8 Downloads

Abstract

The topic of this paper are non-self-adjoint second-order differential operators with a constant delay, which is less than half of the length of the interval. We consider the case when a delay is from \(\tau \in [\frac{2\pi }{5},\frac{\pi }{2})\), and the potential is a real-valued function which satisfy \(q\in L^{2}[0,\pi ]\). The inverse spectral problem of recovering the potential from the spectra of two boundary value problems with Robin boundary conditions has been studied. We have proved that the delay and the potential are uniquely determined by two spectra of boundary spectral problem, one with boundary conditions \(y'(0)-hy(0)=0\), \(y'(\pi )+H_{1} y(\pi )=0\) and the other with boundary conditions \(y'(0)-hy(0)=0\), \(y'(\pi )+H_{2} y(\pi )=0\).

Keywords

Differential operator with a delay inverse spectral problem Fourier coefficients Volterra integral equation 

Mathematics Subject Classification

34A55 34B24 

Notes

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Milenko Pikula
    • 1
  • Vladimir Vladičić
    • 1
    Email author
  • Biljana Vojvodić
    • 2
  1. 1.University of East SarajevoEast SarajevoBosnia and Herzegovina
  2. 2.University of Banja LukaBanja LukaBosnia and Herzegovina

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