Abstract
We prove that if the Neumann eigenvalues of the impulsive Sturm–Liouville operator
Funding source: National Natural Science Foundation of China
Award Identifier / Grant number: 11871031
Funding source: Natural Science Foundation of Jiangsu Province
Award Identifier / Grant number: BK 20201303
Funding statement: The research work was supported in part by the National Natural Science Foundation of China (11871031) and the Natural Science Foundation of Jiangsu Province (BK 20201303).
Acknowledgements
The authors would like to thank the referees for valuable comments.
References
[1] V. A. Ambarzumyan, Über eine Frage der Eigenwerttheorie, Z. Phys. 53 (1929), 690–695. 10.1007/BF01330827Search in Google Scholar
[2] G. Borg, Eine Umkehrung der Sturm–Liouvilleschen Eigenwertaufgabe. Bestimmung der Differentialgleichung durch die Eigenwerte, Acta Math. 78 (1946), 1–96. 10.1007/BF02421600Search in Google Scholar
[3] R. Carlson and V. Pivovarchik, Ambarzumian’s theorem for trees, Electron. J. Differential Equations 2007 (2007), Paper No. 142. Search in Google Scholar
[4] G. Freiling and V. Yurko, Inverse Sturm–Liouville Problems and Their Applications, Nova Science, Huntington, 2001. Search in Google Scholar
[5] M. Horváth, On a theorem of Ambarzumian, Proc. Roy. Soc. Edinburgh Sect. A 131 (2001), no. 4, 899–907. 10.1017/S0308210500001177Search in Google Scholar
[6] M. Horváth, On the stability in Ambarzumian theorems, Inverse Problems 31 (2015), Article ID 025008. 10.1088/0266-5611/31/2/025008Search in Google Scholar
[7] H. M. Huseynov and F. Z. Dostuyev, On determination of Sturm–Liouville operator with discontinuity conditions with respect to spectral data, Proc. Inst. Math. Mech. Natl. Acad. Sci. Azerb. 42 (2016), no. 2, 143–153. Search in Google Scholar
[8] R. J. Krueger, Inverse problems for nonabsorbing media with discontinuous material properties, J. Math. Phys. 23 (1982), no. 3, 396–404. 10.1063/1.525358Search in Google Scholar
[9] C.-K. Law and E. Yanagida, A solution to an Ambarzumyan problem on trees, Kodai Math. J. 35 (2012), no. 2, 358–373. 10.2996/kmj/1341401056Search in Google Scholar
[10] V. A. Marchenko, Sturm–Liouville Operators and Applications, Oper. Theory Adv. Appl. 22, Birkhäuser, Basel, 1986. 10.1007/978-3-0348-5485-6Search in Google Scholar
[11] K. Márton, An n-dimensional Ambarzumyan type theorem for Dirac operators, Inverse Problems 20 (2004), 1593–1797. 10.1088/0266-5611/20/5/016Search in Google Scholar
[12] A. A. Nabiev, M. Gürdal and S. Saltan, Inverse problems for the Sturm–Liouville equation with the discontinuous coefficient, J. Appl. Anal. Comput. 7 (2017), no. 2, 559–580. 10.11948/2017035Search in Google Scholar
[13] A. S. Ozkan, B. Keskin and Y. Cakmak, Uniqueness of the solution of half inverse problem for the impulsive Sturm Liouville operator, Bull. Korean Math. Soc. 50 (2013), no. 2, 499–506. 10.4134/BKMS.2013.50.2.499Search in Google Scholar
[14] V. N. Pivovarchik, Ambartsumyan’s theorem for the Sturm–Liouville boundary value problem on a star-shaped graph, Funktsional. Anal. i Prilozhen. 39 (2005), no. 2, 78–81. 10.1007/s10688-005-0029-1Search in Google Scholar
[15] A. G. Ramm and P. D. Stefanov, A three-dimensional Ambartsumian-type theorem, Appl. Math. Lett. 5 (1992), no. 5, 87–88. 10.1016/0893-9659(92)90072-HSearch in Google Scholar
[16] C.-F. Yang and X.-P. Yang, Some Ambarzumyan-type theorems for Dirac operators, Inverse Problems 25 (2009), no. 9, Article ID 095012. 10.1088/0266-5611/25/9/095012Search in Google Scholar
[17] V. Yurko, Inverse spectral problems for Sturm–Liouville operators with complex weights, Inverse Probl. Sci. Eng. 26 (2018), no. 10, 1396–1403. 10.1080/17415977.2017.1400030Search in Google Scholar
[18] V. A. Yurko, On Ambarzumyan-type theorems, Appl. Math. Lett. 26 (2013), no. 4, 506–509. 10.1016/j.aml.2012.12.006Search in Google Scholar
© 2021 Walter de Gruyter GmbH, Berlin/Boston
