[1] V. Ambarzumjan, Über eine Frage der Eigenwerttheorie, Z. Phys. 53, 690–695, 1929.
[2] G. Borg, Eine Umkehrung der Sturm-Liouvilleschen Eigenwertaufgabe: Bestimmung
der Differentialgleichung durch die Eigenwerte, Acta Math. 78, 1–96, 1946.
[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 (1), 17–27, 2019.
[4] M. Pikula, Opredelenie differencial’nogo operatora tipa Šturma-Liuvillya s zapazdyvayusim argumentom po dvum spektram, Mat. Vesnik 43, 159–171, 1991.
[5] M. Pikula, E. Čatrnja, and I. Kalčo, Spectral problems for operators with deviating
arguments, Hacet. J. Math. Stat. 47 (5), 1172–1183, 2018.
[6] M. Pikula, D. Nedić, and E. Čatrnja, Partial invese spectral problems for the Sturm-
Liouville operator with delay, Sarajevo J. Math. 16 (29), 41–54, 2020.
[7] M. Pikula, V. Vladičić, and D. Nedić, Inverse Sturm-Liouville problems with homogeneous delay, Siberian Math. J. 55 (2), 301-308, 2014.
[8] M. Pikula, V. Vladičić, and B. Vojvodić, Inverse spectral problem for Sturm-Liouville
operators with a constant delay less than half the length of the interval and Robin
boundary conditions, Results Math. 74 (1), 45, 2019.
[9] V. Vladičić and N. Djurić, Incomplete inverse problem for SturmLiouville type differential equation with constant delay, Results Math. 74 (4), 161, 2019.
[10] V. Vladičić and M. Pikula, An inverse problems for Sturm-Liouville-type differential
equation with a constant delay, Sarajevo J. Math. 12 (24), 83-88, 2016.
[11] V.A. Yurko, Recovering differential operators with a retarded argument, Differ. Equ.
55 (4), 510–514, 2019.
[12] V.A. Yurko, S.A. Buterin, and M. Pikula, Sturm-Liouville differential operators with
deviating argument, Tamkang J. Math. 48 (1), 49–59, 2017.
Spectral properties of some differential operators of Sturm-Liouville type with homogeneous delay
Year 2022,
Volume: 51 Issue: 3, 658 - 665, 01.06.2022
In this paper we observe the operator $ D^{2}=D^{2}(h,H,q,\alpha)$, $h, H\in \overline{\mathbb{R}}=\mathbb{R}\cup \{-\infty,\infty\}$, $q(x)\in L_{2}\left[0,\pi \right]$, $\alpha\in (0,1) $ and construct and partially transform its characteristic function. Those transformations enable more complete asymptotic decomposition of the zeroes and eigenvalues of the operator.
The goal of this paper is to contribute to the development of the spectral theory of differential operators with homogeneous delay.
[1] V. Ambarzumjan, Über eine Frage der Eigenwerttheorie, Z. Phys. 53, 690–695, 1929.
[2] G. Borg, Eine Umkehrung der Sturm-Liouvilleschen Eigenwertaufgabe: Bestimmung
der Differentialgleichung durch die Eigenwerte, Acta Math. 78, 1–96, 1946.
[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 (1), 17–27, 2019.
[4] M. Pikula, Opredelenie differencial’nogo operatora tipa Šturma-Liuvillya s zapazdyvayusim argumentom po dvum spektram, Mat. Vesnik 43, 159–171, 1991.
[5] M. Pikula, E. Čatrnja, and I. Kalčo, Spectral problems for operators with deviating
arguments, Hacet. J. Math. Stat. 47 (5), 1172–1183, 2018.
[6] M. Pikula, D. Nedić, and E. Čatrnja, Partial invese spectral problems for the Sturm-
Liouville operator with delay, Sarajevo J. Math. 16 (29), 41–54, 2020.
[7] M. Pikula, V. Vladičić, and D. Nedić, Inverse Sturm-Liouville problems with homogeneous delay, Siberian Math. J. 55 (2), 301-308, 2014.
[8] M. Pikula, V. Vladičić, and B. Vojvodić, Inverse spectral problem for Sturm-Liouville
operators with a constant delay less than half the length of the interval and Robin
boundary conditions, Results Math. 74 (1), 45, 2019.
[9] V. Vladičić and N. Djurić, Incomplete inverse problem for SturmLiouville type differential equation with constant delay, Results Math. 74 (4), 161, 2019.
[10] V. Vladičić and M. Pikula, An inverse problems for Sturm-Liouville-type differential
equation with a constant delay, Sarajevo J. Math. 12 (24), 83-88, 2016.
[11] V.A. Yurko, Recovering differential operators with a retarded argument, Differ. Equ.
55 (4), 510–514, 2019.
[12] V.A. Yurko, S.A. Buterin, and M. Pikula, Sturm-Liouville differential operators with
deviating argument, Tamkang J. Math. 48 (1), 49–59, 2017.
Nedić, D., & Catrnja, E. (2022). Spectral properties of some differential operators of Sturm-Liouville type with homogeneous delay. Hacettepe Journal of Mathematics and Statistics, 51(3), 658-665. https://doi.org/10.15672/hujms.817504
AMA
Nedić D, Catrnja E. Spectral properties of some differential operators of Sturm-Liouville type with homogeneous delay. Hacettepe Journal of Mathematics and Statistics. June 2022;51(3):658-665. doi:10.15672/hujms.817504
Chicago
Nedić, Dragana, and Elmir Catrnja. “Spectral Properties of Some Differential Operators of Sturm-Liouville Type With Homogeneous Delay”. Hacettepe Journal of Mathematics and Statistics 51, no. 3 (June 2022): 658-65. https://doi.org/10.15672/hujms.817504.
EndNote
Nedić D, Catrnja E (June 1, 2022) Spectral properties of some differential operators of Sturm-Liouville type with homogeneous delay. Hacettepe Journal of Mathematics and Statistics 51 3 658–665.
IEEE
D. Nedić and E. Catrnja, “Spectral properties of some differential operators of Sturm-Liouville type with homogeneous delay”, Hacettepe Journal of Mathematics and Statistics, vol. 51, no. 3, pp. 658–665, 2022, doi: 10.15672/hujms.817504.
ISNAD
Nedić, Dragana - Catrnja, Elmir. “Spectral Properties of Some Differential Operators of Sturm-Liouville Type With Homogeneous Delay”. Hacettepe Journal of Mathematics and Statistics 51/3 (June 2022), 658-665. https://doi.org/10.15672/hujms.817504.
JAMA
Nedić D, Catrnja E. Spectral properties of some differential operators of Sturm-Liouville type with homogeneous delay. Hacettepe Journal of Mathematics and Statistics. 2022;51:658–665.
MLA
Nedić, Dragana and Elmir Catrnja. “Spectral Properties of Some Differential Operators of Sturm-Liouville Type With Homogeneous Delay”. Hacettepe Journal of Mathematics and Statistics, vol. 51, no. 3, 2022, pp. 658-65, doi:10.15672/hujms.817504.
Vancouver
Nedić D, Catrnja E. Spectral properties of some differential operators of Sturm-Liouville type with homogeneous delay. Hacettepe Journal of Mathematics and Statistics. 2022;51(3):658-65.