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On recovering Sturm–Liouville operators with two delays

  • Biljana Vojvodić und Vladimir Vladičić EMAIL logo
Veröffentlicht/Copyright: 15. Mai 2024

Abstract

We study the inverse spectral problems of recovering Sturm–Liouville differential operator with two constant delays a 1 and a 2 greater than one third of the interval. It has been proved that the operator can be recovered uniquely from four spectra under the condition 2 a 1 + a 2 2 π , while it is not possible otherwise.

MSC 2020: 34A55; 34K29

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.2018.03.025Suche in Google Scholar

[2] S. A. Buterin, M. A. Malyugina and C.-T. Shieh, An inverse spectral problem for second-order functional-differential pencils with two delays, Appl. Math. Comput. 411 (2021), Article ID 126475. 10.1016/j.amc.2021.126475Suche in Google Scholar

[3] 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/s13324-017-0176-6Suche in Google Scholar

[4] N. Djurić and S. Buterin, On an open question in recovering Sturm–Liouville-type operators with delay, Appl. Math. Lett. 113 (2021), Article ID 106862. 10.1016/j.aml.2020.106862Suche in Google Scholar

[5] N. Djurić and S. Buterin, On non-uniqueness of recovering Sturm–Liouville operators with delay, Commun. Nonlinear Sci. Numer. Simul. 102 (2021), Article ID 105900. 10.1016/j.cnsns.2021.105900Suche in Google Scholar

[6] N. Djurić and S. Buterin, Iso-bispectral potentials for Sturm–Liouville-type operators with small delay, Nonlinear Anal. Real World Appl. 63 (2022), Article ID 103390. 10.1016/j.nonrwa.2021.103390Suche in Google Scholar

[7] N. Djurić and V. Vladičić, Incomplete inverse problem for Sturm–Liouville type differential equation with constant delay, Results Math. 74 (2019), no. 4, Paper No. 161. 10.1007/s00025-019-1087-7Suche in Google Scholar

[8] G. Freiling and V. Yurko, Inverse Sturm–Liouville Problems and Their Applications, Nova Science, Huntington, 2001. Suche in Google Scholar

[9] 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.2012.03.026Suche in Google Scholar

[10] 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/FIL1501051PSuche in Google Scholar

[11] M. Pikula, Determination of a Sturm–Liouville-type differential operator with retarded argument from two spectra, Mat. Vesnik 43 (1991), no. 3–4, 159–171. Suche in Google Scholar

[12] 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, Paper No. 45. 10.1007/s00025-019-0972-4Suche in Google Scholar

[13] V. Vladičić, M. Bošković and B. Vojvodić, Inverse problems for Sturm–Liouville-type differential equation with a constant delay under Dirichlet/polynomial boundary conditions, Bull. Iranian Math. Soc. 48 (2022), no. 4, 1829–1843. 10.1007/s41980-021-00616-5Suche in Google Scholar

[14] 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.12.1.06Suche in Google Scholar

[15] B. Vojvodić and N. Pavlović Komazec, Inverse problems for Sturm–Liouville operator with potential functions from L 2 [ 0 , π ] , Math. Montisnigri 49 (2020), 28–38. 10.20948/mathmontis-2020-49-2Suche in Google Scholar

[16] B. Vojvodić, N. Pavlović Komazec and F. A. Çetinkaya, Recovering differential operators with two retarded arguments, Bol. Soc. Mat. Mex. (3) 28 (2022), no. 3, Paper No. 68. 10.1007/s40590-022-00462-3Suche in Google Scholar

[17] B. Vojvodic, M. Pikula and V. Vladicic, Inverse problems for Sturm–Liouville differential operators with two constant delays under Robin boundary conditions, Results Appl. Math. 5 (2020), Article ID 100082. 10.1016/j.rinam.2019.100082Suche in Google Scholar

[18] B. Vojvodic, M. Pikula, V. Vladicic and F. A. Çetinkaya, Inverse problems for differential operators with two delays larger than half the length of the interval and Dirichlet conditions, Turkish J. Math. 44 (2020), no. 3, 900–905. 10.3906/mat-1903-112Suche in Google Scholar

[19] B. M. Vojvodic and V. M. Vladicic, Recovering differential operators with two constant delays under Dirichlet/Neumann boundary conditions, J. Inverse Ill-Posed Probl. 28 (2020), no. 2, 237–241. 10.1515/jiip-2019-0074Suche in Google Scholar

[20] V. Yurko, Recovering differential operators with a retarded argument, Differ. Uravn. 55 (2019), no. 5, 524–528, translation in Differ. Equ. 5 (2019), no. 4, 510–514. 10.1134/S0012266119040086Suche in Google Scholar

Received: 2023-12-12
Accepted: 2024-04-07
Published Online: 2024-05-15
Published in Print: 2024-12-01

© 2024 Walter de Gruyter GmbH, Berlin/Boston

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