Determination of the impulsive Sturm–Liouville operator from a set of eigenvalues

References

[1] R. K. Amirov, On Sturm–Liouville operators with discontinuity conditions inside an interval, J. Math. Anal. Appl. 317 (2006), no. 1, 163–176. 10.1016/j.jmaa.2005.11.042Search in Google Scholar

[2] R. S. Anderssen, The effect of discontinuities in density and shear velocity on the asymptotic overtone structure of tortional eigenfrequencies of the Earth, Geophys J. R. Astr. Soc. 50 (1997), 303–309. 10.1111/j.1365-246X.1977.tb04175.xSearch in Google Scholar

[3] L.-E. Andersson, Inverse eigenvalue problems with discontinuous coefficients, Inverse Problems 4 (1988), no. 2, 353–397. 10.1088/0266-5611/4/2/004Search in Google Scholar

[4] S. A. Buterin, G. Freiling and V. A. Yurko, Lectures in the theory of entire functions, Schriftenreihe der Fakultät für Matematik SM-UDE-779, Duisbug–Essen University, 2014. Search in Google Scholar

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

[6] Y. Guo, G. Wei and R. Yao, Inverse problem for interior spectral data of discontinuous Dirac operator, Appl. Math. Comput. 268 (2015), 775–782. 10.1016/j.amc.2015.06.091Search in Google Scholar

[7] O. H. Hald, Discontinuous inverse eigenvalue problems, Comm. Pure Appl. Math. 37 (1984), no. 5, 539–577. 10.1002/cpa.3160370502Search in Google Scholar

[8] H. Hochstadt and B. Lieberman, An inverse Sturm–Liouville problem with mixed given data, SIAM J. Appl. Math. 34 (1978), no. 4, 676–680. 10.1137/0134054Search in Google Scholar

[9] R. O. Hryniv and Y. V. Mykytyuk, Half-inverse spectral problems for Sturm–Liouville operators with singular potentials, Inverse Problems 20 (2004), no. 5, 1423–1444. 10.1088/0266-5611/20/5/006Search in Google Scholar

[10] 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

[11] O. Martinyuk and V. Pivovarchik, On the Hochstadt–Lieberman theorem, Inverse Problems 26 (2010), no. 3, Article ID 035011. 10.1088/0266-5611/26/3/035011Search in Google Scholar

[12] K. Mochizuki and I. Trooshin, Inverse problem for interior spectral data of the Sturm–Liouville operator, J. Inverse Ill-Posed Probl. 9 (2001), no. 4, 425–433. 10.1515/jiip.2001.9.4.425Search in Google Scholar

[13] K. Mochizuki and I. Trooshin, Inverse problem for interior spectral data of the Dirac operator on a finite interval, Publ. Res. Inst. Math. Sci. 38 (2002), no. 2, 387–395. 10.2977/prims/1145476343Search in Google Scholar

[14] A. A. Nabiev and R. K. Amirov, On the boundary value problem for the Sturm–Liouville equation with the discontinuous coefficient, Math. Methods Appl. Sci. 36 (2013), no. 13, 1685–1700. 10.1002/mma.2714Search in Google Scholar

[15] 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

[16] W. Rundell and P. E. Sacks, Reconstruction techniques for classical inverse Sturm–Liouville problems, Math. Comp. 58 (1992), no. 197, 161–183. 10.1090/S0025-5718-1992-1106979-0Search in Google Scholar

[17] W. Rundell and P. E. Sacks, Reconstruction of a radially symmetric potential from two spectral sequences, J. Math. Anal. Appl. 264 (2001), no. 2, 354–381. 10.1006/jmaa.2001.7664Search in Google Scholar

[18] L. Sakhnovich, Half-inverse problems on the finite interval, Inverse Problems 17 (2001), no. 3, 527–532. 10.1088/0266-5611/17/3/311Search in Google Scholar

[19] C.-T. Shieh and V. A. Yurko, Inverse nodal and inverse spectral problems for discontinuous boundary value problems, J. Math. Anal. Appl. 347 (2008), no. 1, 266–272. 10.1016/j.jmaa.2008.05.097Search in Google Scholar

[20] C. Willis, Inverse Sturm–Liouville problems with two discontinuities, Inverse Problems 1 (1985), no. 3, 263–289. 10.1088/0266-5611/1/3/010Search in Google Scholar

[21] X.-C. Xu and C.-F. Yang, Inverse spectral problems for the Sturm–Liouville operator with discontinuity, J. Differential Equations 262 (2017), no. 3, 3093–3106. 10.1016/j.jde.2016.11.024Search in Google Scholar

[22] X.-C. Xu and C.-F. Yang, Reconstruction of the Sturm–Liouville operator with discontinuities from a particular set of eigenvalues, Appl. Math. J. Chinese Univ. Ser. B 33 (2018), no. 2, 225–233. 10.1007/s11766-018-3533-9Search in Google Scholar

[23] C.-F. Yang, An interior inverse problem for discontinuous boundary-value problems, Integral Equations Operator Theory 65 (2009), no. 4, 593–604. 10.1007/s00020-009-1693-ySearch in Google Scholar

[24] C.-F. Yang, Hochstadt–Lieberman theorem for Dirac operator with eigenparameter dependent boundary conditions, Nonlinear Anal. 74 (2011), no. 7, 2475–2484. 10.1016/j.na.2010.12.003Search in Google Scholar

[25] C.-F. Yang and X.-P. Yang, An interior inverse problem for the Sturm–Liouville operator with discontinuous conditions, Appl. Math. Lett. 22 (2009), no. 9, 1315–1319. 10.1016/j.aml.2008.12.001Search in Google Scholar

[26] V. A. Yurko, Integral transforms connected with discontinuous boundary value problems, Integral Transform. Spec. Funct. 10 (2000), no. 2, 141–164. 10.1080/10652460008819282Search in Google Scholar

[27] V. A. Yurko, On boundary value problems with discontinuity conditions inside an interval, Differ. Uravn. 36 (2000), no. 8, 1139–1140, 1152. 10.1007/BF02754199Search in Google Scholar

[28] V. A. 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