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Recovering differential operators with two constant delays under Dirichlet/Neumann boundary conditions

  • Biljana M. Vojvodic and Vladimir M. Vladicic EMAIL logo

Abstract

This paper deals with non-self-adjoint differential operators with two constant delays generated by -y′′+q1(x)y(x-τ1)+(-1)iq2(x)y(x-τ2), where π3τ2<π2<2τ2τ1<π and potentials qj are real-valued functions, qjL2[0,π]. We will prove that the delays and the potentials are uniquely determined from the spectra of four boundary value problems: two of them under boundary conditions y(0)=y(π)=0 and the remaining two under boundary conditions y(0)=y(π)=0.

MSC 2010: 34B24; 34B09; 34L10

Funding statement: This research is partially supported by a grant of the Ministry for Scientific and Technological Development, Higher Education and Information Society of the Republic of Srpska.

References

[1] N. Bondarenko and V. Yurko, An inverse problem for Sturm–Liouville differential operators with deviating argument, Appl. Math. Lett. 83 (2018), 140–144. 10.1016/j.aml.2018.03.025Search in Google Scholar

[2] S. A. Buterin and V. A. Yurko, An inverse spectral problem for Sturm–Liouville operators with a large constant delay, Anal. Math. Phys. 9 (2019), no. 1, 17–27. 10.1007/s13324-017-0176-6Search in Google Scholar

[3] G. Freiling and V. Yurko, Inverse Sturm–Liouville problems and their applications, Nova Science Publishers, Inc., Huntington, NY, 2001. Search in Google Scholar

[4] G. Freiling and V. A. Yurko, Inverse problems for Sturm–Liouville differential operators with a constant delay, Appl. Math. Lett. 25 (2012), no. 11, 1999–2004. 10.1016/j.aml.2012.03.026Search in Google Scholar

[5] N. Pavlović, M. Pikula and B. Vojvodić, First regularized trace of the limit assignment of Sturm–Liouville type with two constant delays, Filomat 29 (2015), no. 1, 51–62. 10.2298/FIL1501051PSearch in Google Scholar

[6] M. Pikula, V. Vladičić and B. Vojvodić, Inverse spectral problems for Sturm–Liouville operators with a constant delay less than half the length of the interval and Robin boundary conditions, Results Math. 74 (2019), no. 1, Article No. 45. 10.1007/s00025-019-0972-4Search in Google Scholar

[7] M. Shahriari, Inverse problem for Sturm–Liouville differential operators with two constant delays, Turkish J. Math. 43 (2019), no. 2, 965–976. 10.3906/mat-1811-113Search in Google Scholar

[8] V. Vladičić and M. Pikula, An inverse problems for Sturm–Liouville-type differential equation with a constant delay, Sarajevo J. Math. 12(24) (2016), no. 1, 83–88. 10.5644/SJM.12.1.06Search in Google Scholar

[9] B. Vojvodich and M. Pikula, A boundary value problem for a differential operator of Sturm–Liouville type under N constant delays, and eigenvalue asymptotics, Math. Montisnigri 35 (2016), 5–21. Search in Google Scholar

[10] V. Yurko, Recovering differential operators with a retarded argument, Differ. Equ. 55 (2019), no. 4, 510–514, translation of Differ. Uravn. 55 (2019), no. 4, 524–528. 10.1134/S0012266119040086Search in Google Scholar

Received: 2019-10-15
Accepted: 2019-11-27
Published Online: 2019-12-19
Published in Print: 2020-04-01

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