A uniqueness result for differential pencils with discontinuities from interior spectral data

References

[1] D. Alpay and I. Gohberg, Inverse problems associated to a canonical differential system, Recent Advances in Operator Theory and Related Topics (Szeged 1999), Oper. Theory Adv. Appl. 127, Birkhäuser, Basel (2001), 1–27. 10.1007/978-3-0348-8374-0_1Search in Google Scholar

[2] E. Bairamov and C. Coskun, Jost solutions and the spectrum of the system of difference equations, Appl. Math. Lett. 17 (2004), no. 9, 1039–1045. 10.1016/j.aml.2004.07.006Search in Google Scholar

[3] L. Collatz, Eigenwertaufgaben mit technischen Anwendungen, Akademische Verlagsgesellschaft Geest & Portig, Leipzig, 1963. Search in Google Scholar

[4] J. B. Conway, Functions of one Complex Variable. II, Grad. Texts in Math. 159, Springer, New York, 1995. 10.1007/978-1-4612-0817-4Search 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] M. G. Gasymov and G. v. Guseĭnov, Determination of a diffusion operator from spectral data, Akad. Nauk Azerbaĭdzhan. SSR Dokl. 37 (1981), no. 2, 19–23. Search in Google Scholar

[7] I. M. Gel’fand and B. M. Levitan, On the determination of a differential equation from its spectral function, Izv. Akad. Nauk SSSR. Ser. Mat. 15 (1951), 309–360. 10.1007/978-3-642-61705-8_24Search in Google Scholar

[8] T. Gulsen and E. Yilmaz, Inverse nodal problem for p-Laplacian diffusion equation with polynomially dependent spectral parameter, Commun. Fac. Sci. Univ. Ank. Sér. A1 Math. Stat. 65 (2016), no. 2, 23–36. 10.1501/Commua1_0000000756Search in Google Scholar

[9] M. Jaulent and C. Jean, The inverse s-wave scattering problem for a class of potentials depending on energy, Comm. Math. Phys. 28 (1972), 177–220. 10.1007/BF01645775Search in Google Scholar

[10] P. Jonas, On the spectral theory of operators associated with perturbed Klein–Gordon and wave type equations, J. Operator Theory 29 (1993), no. 2, 207–224. Search in Google Scholar

[11] H. Koyunbakan, A new inverse problem for the diffusion operator, Appl. Math. Lett. 19 (2006), no. 10, 995–999. 10.1016/j.aml.2005.09.014Search in Google Scholar

[12] H. Koyunbakan, The inverse nodal problem for a differential operator with an eigenvalue in the boundary condition, Appl. Math. Lett. 21 (2008), no. 12, 1301–1305. 10.1016/j.aml.2008.01.003Search in Google Scholar

[13] H. Koyunbakan, The transmutation method and Schrödinger equation with perturbed exactly solvable potential, J. Comput. Acoust. 17 (2009), no. 1, 1–10. 10.1142/S0218396X09003823Search in Google Scholar

[14] H. Koyunbakan and E. S. Panakhov, Half-inverse problem for diffusion operators on the finite interval, J. Math. Anal. Appl. 326 (2007), no. 2, 1024–1030. 10.1016/j.jmaa.2006.03.068Search in Google Scholar

[15] F. R. Lapwood and T. Usami, Free Oscillations of the Earth, Cambridge University Press, Cambridge, 1981. Search in Google Scholar

[16] R. Mennicken and M. Möller, Non-self-adjoint Boundary Eigenvalue Problems, North-Holland Math. Stud. 192, North-Holland, Amsterdam, 2003. 10.1016/S0304-0208(03)80005-1Search in Google Scholar

[17] 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

[18] A. Neamaty and Y. Khalili, Determination of a differential operator with discontinuity from interior spectral data, Inverse Probl. Sci. Eng. 22 (2014), no. 6, 1002–1008. 10.1080/17415977.2013.848436Search in Google Scholar

[19] A. Neamaty and Y. Khalili, The inverse problem for pencils of differential operators on the half-line with discontinuity, Malays. J. Math. Sci. 9 (2015), no. 2, 175–186. Search in Google Scholar

[20] J. Pöschel and E. Trubowitz, Inverse Spectral Theory, Pure Appl. Math. 130, Academic Press, Boston, 1987. Search in Google Scholar

[21] V. S. Rykhlov, Asymptotical formulas for solutions of linear differential systems of the first order, Results Math. 36 (1999), no. 3–4, 342–353. 10.1007/BF03322121Search in Google Scholar

[22] L. K. Sharma, P. V. Luhanga and S. Chimidza, Potentials for the Klein–Gordon and Dirac equations, Chiang Mai J. Sci. 38 (2011), no. 4, 514–526. Search in Google Scholar

[23] A. A. Shkalikov, Boundary problems for ordinary differential equations with parameter in the boundary conditions, J. Sov. Math. 33 (1986), 1311–1342. 10.1007/BF01084754Search in Google Scholar

[24] A. Wazwaz, Partial Differential Equations Methods and Applications, Balkema, Leiden, 2002. Search in Google Scholar

[25] C.-F. Yang and Y.-X. Guo, Determination of a differential pencil from interior spectral data, J. Math. Anal. Appl. 375 (2011), no. 1, 284–293. 10.1016/j.jmaa.2010.09.011Search in Google Scholar

[26] 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

[27] C.-F. Yang and A. Zettl, Half inverse problems for quadratic pencils of Sturm–Liouville operators, Taiwanese J. Math. 16 (2012), no. 5, 1829–1846. 10.11650/twjm/1500406800Search in Google Scholar

[28] E. Yilmaz, Lipschitz stability of inverse nodal problem for energy-dependent Sturm–Liouville equation, New Trends Math. Sci. 3 (2015), no. 1, 46–61. 10.1186/s13661-015-0298-4Search in Google Scholar

[29] V. Yurko, Inverse spectral problems for differential pencils on the half-line with turning points, J. Math. Anal. Appl. 320 (2006), no. 1, 439–463. 10.1016/j.jmaa.2005.06.085Search in Google Scholar