Inverse problems for the impulsive Sturm–Liouville operator with jump conditions

References

• Baltes HP. Inverse scattering problems in optics. Berlin: Springer; 1980. (Topics in current physics).
   Google Scholar
• Hogben L. Spectral graph theory and inverse eigenvalue problem of a graph. Chamchuri J Math. 2009;1(1):51–72.
   Google Scholar
• Johnson CR, Leal-Duarte A, Saiago CM. Inverse eigenvalue problems and lists of multiplicities of eigengvalues for matrices whose graph is a tree: the case of generalized stars and double generalized stars. Linear Algebra Appl. 2003;373:311–330. doi: 10.1016/S0024-3795(03)00582-2
   Web of Science ®Google Scholar
• Parker RL, Whaler KA. Numerical methods for establishing solutions to the inverse problem of electromagnetic induction. J Geophys Res. 1981;86(10):9574–9584. doi: 10.1029/JB086iB10p09574
   Google Scholar
• Gelfand IM, Levitan BM. On the determination of a differential equation from its spectral function. Izv Akad Nauk SSR Ser Mat. 1951;15:309–360.
   Google Scholar
• Koyunbakan H. The inverse nodal problem for a differential operator with an eigenvalue in the boundary condition. Appl Math Lett. 2008;21:1301–1305. doi: 10.1016/j.aml.2008.01.003
   Web of Science ®Google Scholar
• Yang CF, Guo YX. Determination of a differential pencil from interior spectral data. J Math Anal Appl. 2011;375:284–293. doi: 10.1016/j.jmaa.2010.09.011
   Web of Science ®Google Scholar
• Yurko V. Inverse spectral problems for differential pencils on the half-line with turning points. J Math Anal Appl. 2006;320:439–463. doi: 10.1016/j.jmaa.2005.06.085
   Web of Science ®Google Scholar
• Hald O. Discontinuous inverse eigenvalue problems. Commun Pure Appl Math. 1984;37(5):539–577. doi: 10.1002/cpa.3160370502
   Web of Science ®Google Scholar
• Neamaty A, Khalili Y. Determination of a differential operator with discontinuity from interior spectral data. Inverse Probl Sci Eng. 2013;22(6):1002–1008. doi: 10.1080/17415977.2013.848436
   Web of Science ®Google Scholar
• Shahriari M, Jodayree A, Teschi G. Uniqueness for inverse Sturm–Liouville problems with a finite number of transmission condition. J Math Anal Appl. 2012;395(1):19–29. doi: 10.1016/j.jmaa.2012.04.048
   Web of Science ®Google Scholar
• Wang YP, Yang CF, Huang ZY. Half inverse problem for Sturm–Liouville operators with boundary conditions dependent on the spectral parameter. Turkish J Math. 2013;37:445–454.
   Web of Science ®Google Scholar
• Willis C. Inverse Sturm–Liouville problems with two discontinuities. Inverse Probl. 1985;1(3):263–289. doi: 10.1088/0266-5611/1/3/010
   Web of Science ®Google Scholar
• Yang CF, Yang XP. An interior inverse problem for the Sturm–Liouville operator with discontinuous conditions. Appl Math Lett. 2009;22:1315–1319. doi: 10.1016/j.aml.2008.12.001
   Web of Science ®Google Scholar
• Freiling G, Yurko VA. Inverse Sturm–Liouville problems and their applications. New York: NOVA Scince Publ.; 2001.
   Google Scholar
• Freiling G, Yurko V. Recovering nonselfadjoint differential pencils with nonseparated boundary conditions. Appl Anal. 2015;94(8):1649–1661. doi: 10.1080/00036811.2014.940918
   Web of Science ®Google Scholar
• Mochizuki K, Trooshin I. Inverse problem for interior spectral data of Sturm–Liouville operator. J Inverse Ill-Posed Probl. 2001;9:425–433. doi: 10.1515/jiip.2001.9.4.425
   Google Scholar
• Mochizuki K, Trooshin I. Inverse problem for interior spectral data of the Dirac operator on a finite interval. Publ Res Inst Math Sci, Kyoto Univ. 2002;38(2):387–395. doi: 10.2977/prims/1145476343
   Web of Science ®Google Scholar
• Sat M, Panakhov ES. A uniqueness theorem for Bessel operator from interior spectral data. Abstr Appl Anal. 2013. DOI:10.1155/2013/713654.
   Google Scholar
• Wang YP. An interior inverse problem for Sturm–Liouville operators with eigenparameter dependent boundary conditions. Tamkang J Math. 2011;42:395–403.
   Google Scholar
• Gesztesy F, Simon B. Inverse spectral analysis with partial information on the potential, II. The case of discrete spectrum. Trans Am Math Soc. 2000;352:2765–2787. doi: 10.1090/S0002-9947-99-02544-1
   Web of Science ®Google Scholar
• Horvath M. Inverse spectral problems and closed exponential systems. Ann Math. 2005;162:885–918. doi: 10.4007/annals.2005.162.885
   Web of Science ®Google Scholar
• Conway JB. Functions of one complex variable. 2nd ed. Vol. I. New York: Springer-Verlag; 1995.
   Google Scholar
• Wang YP. Uniqueness theorems for Sturm–Liouville operators with boundary conditions polynomially dependent on the eigenparameter from spectral data. Results Math. 2013;63:1131–1144. doi: 10.1007/s00025-012-0258-6
   Web of Science ®Google Scholar