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Half inverse problems for the singular Sturm-Liouville operator | ||
International Journal of Nonlinear Analysis and Applications | ||
مقاله 253، دوره 13، شماره 2، مهر 2022، صفحه 3161-3171 اصل مقاله (386.56 K) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.27348.3569 | ||
نویسندگان | ||
Rauf Amirov؛ Sevim Durak* | ||
Sivas Cumhuriyet University, Faculty of Science, Department of Mathematics, 58140, Turkey | ||
تاریخ دریافت: 10 خرداد 1401، تاریخ بازنگری: 25 خرداد 1401، تاریخ پذیرش: 02 مرداد 1401 | ||
چکیده | ||
In this paper, we consider the inverse spectral problem for the impulsive Sturm-Liouville differential pencils on $\left[ 0,\pi\right] $ with the Robin boundary conditions and the jump conditions at the point $\dfrac{\pi}{2}$. We prove that two potentials functions on the whole interval and the parameters in the boundary and jump conditions can be determined from a set of eigenvalues for two cases: (i) The potentials are given on $\left(0,\dfrac{\pi}{4}\left( \alpha+\beta\right) \right) .$ (ii) The potentials is given on $\left( \dfrac{\pi}{4}\left( \alpha+\beta\right) ,\dfrac{\pi }{2}\left( \alpha+\beta\right) \right) $, where $0<\alpha<\beta<1$ and $\alpha+\beta>1$, respectively. | ||
کلیدواژهها | ||
Inverse spectral problems؛ Sturm-Liouville Operator؛ spectrum؛ uniqueness | ||
مراجع | ||
[1] R.Kh. Amirov, On Sturm-Liouville operators with discontinuity conditions inside an interval, J. Math. Anal. Appl. 317 (2006), no. 1, 163–176. [2] R.Kh. Amirov and A.A. Nabiev, Inverse problems for the quadratic pencil of the Sturm-Liouville equations with impulse, Abstr. Appl. Anal. 2013 (2013), Art.ID 361989, 10 pp. [3] G. Freiling and V.A. Yurko, Inverse spectral problems for singular non-selfadjoint differential operators with discontinuities in an interior point, Inverse Prob. 18 (2002), no. 3, 757–773. [4] O.H. Hald, Discontinuous inverse eigenvalue problems, Commun. Pure Appl. Math. 37 (1984), no. 5, 539–577. [5] H. Hochstadt and B. Lieberman, An inverse Sturm-Liouville problem with mixed given data, SIAM J. Appl. Math. 34 (1978), no. 4, 676–680. [6] R.O. Hryniv and Y.V. Mykytyuk, Half-inverse spectral problems for Sturm-Liouville operators with singular potentials, Inverse Prob. 20 (2004), no. 5, 1423–1444. [7] P. Jonas, On the spectral theory of operators associated with perturbed Klein-Gordon and wave type equations, J. Oper. Theory 29 (1993), 207–224. [8] M.V. Keldyshm, On the eigenvalues and eigenfunctions of some classes of nonselfadjoint equations, Dokl. Akad. Nauk SSSR 77 (1951), 11–14. [9] Y. Khalili and N. Kadkhoda, The interior inverse problem for the impulsive Sturm-Liouville equation, Anal. Math. Phys. 10 (2020), no. 4, 1–10. [10] A.G. Kostyuchenko and A.A. Shkalikov, Selfadjoint quadratic operator pencils and elliptic problems, Funkc. Anal. Prilozh. 17 (1983), 38–61. [11] H. Koyunbakan, Inverse problem for a quadratic pencil of Sturm-Liouville operator, J. Math. Anal. Appl. 378 (2011), 549–554. [12] R.J. Krueger, Inverse problems for nonabsorbing media with discontinuous material properties, J. Math. Phys. 23 (1982), no. 3, 396–404. [13] F.R. Lapwood and T. Usami, Free Oscillation of the Earth, Cambridge University Press, Cambridge, UK, 1981. [14] O.N. Litvinenko and V.I. Soshnikov, The Theory of Heterogeneous Lines and Their Applications in Radio Engineering, Radio, Moscow, Russia, 1964. [15] B.Ya. Levin, Lectures on Entire Functions, Transl. Math. Monographs, 150, Amer. Math. Soc, Providence RI 1996. [16] V.A. Marchenko, Sturm–Liouville Operators and Their Applications, Naukova Dumka, Kiev (1977). English transl., Birkh¨auser, Basel, 1986. [17] O. Martinyuk and V. Pivovarchik, On the Hochstadt-Lieberman theorem, Inverse Prob. 26 (2010), no. 3, Article ID 035011. [18] J.R. McLaughlin, Analytical methods for recovering coefficients in differential equations from spectral data, SIAM Rev. 28 (1986), no. 1, 53–72. [19] V.P. Meshonav and A.I. Feldstein, Automatic Design of Directional Couplers, Sviaz, Moscow, Russian, 1980. [20] A.A. Nabiev and R.Kh. Amirov, On the boundary value problem for the Sturm-Liouville equation with the discontinuous coefficient, Math. Meth. Appl. Sci. 36 (2013), no. 13, 1685–1700. [21] M.A. Ragusa, Parabolic Herz spaces and their applications, Appl. Math. Lett. 25 (2012), no. 10, 1270–1273. [22] W. Rundell and P.E. Sacks, Reconstruction techniques for classical inverse Sturm-Liouville problems, Math. Comp. 58 (1992), no. 197, 161–183. [23] 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. [24] L. Sakhnovich, Half-inverse problems on the finite interval, Inverse Prob. 17 (2001), no. 3, 527–532. [25] D.G. Shepelsky, The inverse problem of reconstruction of the medium’s conductivity in a class of discontinuous and increasing functions, Adv. Soviet Math. 19 (1997), 303–309. [26] V. Vladicic, M. Boskovic and B. Vojvodic, Inverse problems for Sturm-Liouville type differential equation with a constant delay under Dirichlet/Polynomial boundary conditions, Bull. Iran. Math. Soc. 48 (2022), no. 4, 1829–1843. [27] C. Willis, Inverse Sturm-Liouville problems with two discontinuities, Inverse Prob. 1 (1985), no. 3, 263–289. [28] 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. [29] M. Yamamoto, Inverse eigenvalue problem for a vibration of a string with viscous drag, J. Math. Anal. Appl. 152 (1990), 20–34. [30] C.-F. Yang, Hochstadt-Lieberman theorem for Dirac operator with eigenparameter dependent boundary conditions, [32] C.-F. Yang and Y. X. Guo, Determination of a differential pencil from interior spectral data, J. Math. Anal. Appl. 375 (2011), 284–293. [33] 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. [34] V.A. Yurko, On higher-order differential operators with a singular point, Inverse Prob. 9 (1993), no. 4, 495–502. [35] V.A. Yurko, Integral transforms connected with discontinuous boundary value problems, Integral Transform. Spec. Funct. 10 (2000), no. 2, 141–164. [36] R. Zhang, X.-C. Xu, C.-F. Yang and N.P. Boundarenko, Determination of the impulsive Sturm-Liouville operator from a set of eigenvalues, J. Inverse III-Posed Prob. 28 (2020), no. 3, 341–348. | ||
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