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Yıl 2020, Cilt: 5 Sayı: 3, 186 - 198, 30.12.2020

Rauf Amirov Abdullah Ergün

Öz

Kaynakça

  • Referans1. Amirov RK. On Sturm-Liouville operators with discontiniuity conditions inside an interval. Journal of Mathematical Analysis and Aplications. 317(1), 2006, 163-176.
  • Referans2. Amirov RK, Nabiev AA. Inverse problems for the quadratic pencil of the Sturm-Liouville equations with impulse, Abstract Applied Analysis. Art.ID 361989, 2013, 10
  • Referans3. Freiling G, Yurko VA. Inverse spectral problems for singular non-selfadjoint differential operators with discontinuities in an interior point, Inverse Probl.18(3), 2002, 757-773.
  • Referans4. Levin BY. Lectures on Entire Functions, Transl. Math. Monographs. Amer. Math. Soc. Providence. 1996.
  • Referans5. Bellman R. Cooke KL. Differential-Difference Equations. Academic Press. New-York. 1963.
  • Referans6. Zhang R, Xu XC, Yang CF, Bondarenko NP. Determination of the impulsive Sturm-Liouville operator from a set of eigenvalues. J.Inverse and III-Posed Probl. 2019.
  • Referans7. Nabiev AA, Amirov RK. Integral representations for the solutions of the generalized Schroedinger equation in a finite interval, Advances in Pure Mathematics. 5(13), 2015, 777-795.
  • Referans8. Meshonav VP, Feldstein AI. Automatic Design of Directional Couplers. Moscow. Russian. 1980.
  • Referans9. Litvinenko ON, Soshnikov VI. The Theory of Heterogeneous Lines and Their Applications in Radio Engineering. Moscow. Russia. 1964.
  • Referans10. Krueger RJ. Inverse problems for nonabsorbing media with discontinuous material properties. Journal of Mathematical Physics. 23(3), 1982, 396-404.
  • Referans11. Shepelsky DG. The inverse problem of reconstruction of the medium's conductivity in a class of discontinuous and increasing functions. Advances in Soviet Mathematics. 19, 1997, 303-309.
  • Referans12. Lapwood FR, Usami T. Free Oscillation of the Earth. Cambridge University Press. Cambridge. 1981.
  • Referans13. Borg G. Eine Umkehrung der Sturm-Liouvilleschen Eigenwertaufgable. Acta Mathamatica. 78, 1946, 1-96.
  • Referans14. McLaughlin JR. Analytical methods for recovering coefficients in differential equations from spectral data. SIAM. 28(1), 1986, 53-72.
  • Referans15. Hald OH. Discontinuous inverse eigenvalue problems, Communications on Pure and Applied Mathematics. 37(5), 1984, 539-577.
  • Referans16. Yurko VA. On higher-order differantial operators with a singular point. Inverse Problems. 9(4), 1993, 495-502.
  • Referans17. Rundell W, Sacks PE. Reconstruction techniques for classical inverse Sturm-Liouville problems. Math. Comp. 58(197), 1992, 161-183.
  • Referans18. Rundell W, Sacks PE. Reconstruction of a radially symmetric potential from two spectral sequences. J. Math. Anal. Appl. 264(2), 2001, 354-381.
  • Referans19. Yurko VA. Integral transforms connected with discontinuous boundary value problems. Integral Transform. Spec. Funct. 10(2), 2000, 141-164.
  • Referans20. H. Hochstadt H, Lieberman B. An inverse Sturm-Liouville problem with mixed given data. SIAM J. Appl. Math. 34, 1978.
  • Referans21. Hryniv RO, Mykytyuk YV. Half-inverse spectral problems for Sturm-Liouville operators with singular potentials. Inverse Problems. 20(5), 2004, 1423-1444.
  • Referans22. Martinyuk O, Pivovarchik V. On the Hochstadt-Lieberman theorem. Inverse Problems 26(3), 2010, Article ID 035011.
  • Referans23. Sakhnovich L. Half-inverse problems on the finite interval. Inverse Problems. 17(3), 2001, 527-532.
  • Referans24. Ambartsumyan VA. Über eine frage der eigenwerttheorie. Zeitschrift für Physik. 53, 1929, 690-695.
  • Referans25. Xu X-C, Yang C-F. Reconstruction of the Sturm-Liouville operator with discontinuities from a particular set of eigenvalues. Appl. Math. J. Chinese Univ. Ser. B. 33(2), 2018, 225-233.
  • Referans26. Yang C-F. Hochstadt-Lieberman theorem for Dirac operator with eigenparameter dependent boundary conditions. Nonlinear Anal. 74(7), 2011, 2475-2484.
  • Referans27. Koyunbakan H. Inverse problem for a quadratic pencil of Sturm-Liouville operator, J. Math. Anal. Appl. 378, 2011, 549-554.
  • Referans28. Yang C-F, Zettl A. Half inverse problems for quadratic pencils of Stur-Liouville operators. Taiwanese Journal Of Mathematics. 16(5), 2012, 1829-1846.
  • Referans29. Yang C-F, Guo YX. Determination of a differential pencil from interior spectral data. J. Math. Anal. Appl. 375, 2011, 284-293.
  • Referans30. Yang C-F, Yang X-P. An interior inverse problem for the Sturm-Liouville operator with discontinuous conditions. Appl. Math. Lett. 22(9), 2009, 1315-1319.
  • Referans31. Jonas P. On the spectral theory of operators associated with perturbed Klein-Gordon and wave type equations. J. Oper. Theory. 29, 1993, 207-224.
  • Referans32. Keldyshm M. V. On the eigenvalues and eigenfunctions of some classes of nonselffadjoint equations. Dokl. Akad. Nauk SSSR. 77, 1951, 11-14.
  • Referans33. Kostyuchenko AG, Shkalikov AA. Selfadjoint quadratic operator pencils and elliptic problems. Funkc. Anal. Prilozh. 17, 1983, 38-61.
  • Referans34. Marchenko VA. Sturm--Liouville Operators and Their Applications. Naukova Dumka, Kiev (1977). English transl. Birkh\"{a}user. Basel. 1986.
  • Referans35. Yamamoto M. Inverse eigenvalue problem for a vibration of a string with viscous drag. J. Math. Anal. Appl. 152, 1990, 20--34.

Half inverse problems for the impulsive singular diffusion operator

Yıl 2020, Cilt: 5 Sayı: 3, 186 - 198, 30.12.2020

Rauf Amirov Abdullah Ergün

Öz

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 functious 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 is given on $\left(
0,\dfrac{\pi}{4}\left( \alpha+\beta \right) \right) .$ (ii) The potentials is
given on $\left( \alpha+\beta, \dfrac{\alpha+\beta}{2} \right) $, where
$0<\alpha+\beta<1$, $\alpha+\beta>1$ respectively. Finally, was given interior inverse problem for same boundary problem.

Anahtar Kelimeler

Inverse spectral problems Sturm-Liouville Operator spectrum uniqueness

Kaynakça

  • Referans1. Amirov RK. On Sturm-Liouville operators with discontiniuity conditions inside an interval. Journal of Mathematical Analysis and Aplications. 317(1), 2006, 163-176.
  • Referans2. Amirov RK, Nabiev AA. Inverse problems for the quadratic pencil of the Sturm-Liouville equations with impulse, Abstract Applied Analysis. Art.ID 361989, 2013, 10
  • Referans3. Freiling G, Yurko VA. Inverse spectral problems for singular non-selfadjoint differential operators with discontinuities in an interior point, Inverse Probl.18(3), 2002, 757-773.
  • Referans4. Levin BY. Lectures on Entire Functions, Transl. Math. Monographs. Amer. Math. Soc. Providence. 1996.
  • Referans5. Bellman R. Cooke KL. Differential-Difference Equations. Academic Press. New-York. 1963.
  • Referans6. Zhang R, Xu XC, Yang CF, Bondarenko NP. Determination of the impulsive Sturm-Liouville operator from a set of eigenvalues. J.Inverse and III-Posed Probl. 2019.
  • Referans7. Nabiev AA, Amirov RK. Integral representations for the solutions of the generalized Schroedinger equation in a finite interval, Advances in Pure Mathematics. 5(13), 2015, 777-795.
  • Referans8. Meshonav VP, Feldstein AI. Automatic Design of Directional Couplers. Moscow. Russian. 1980.
  • Referans9. Litvinenko ON, Soshnikov VI. The Theory of Heterogeneous Lines and Their Applications in Radio Engineering. Moscow. Russia. 1964.
  • Referans10. Krueger RJ. Inverse problems for nonabsorbing media with discontinuous material properties. Journal of Mathematical Physics. 23(3), 1982, 396-404.
  • Referans11. Shepelsky DG. The inverse problem of reconstruction of the medium's conductivity in a class of discontinuous and increasing functions. Advances in Soviet Mathematics. 19, 1997, 303-309.
  • Referans12. Lapwood FR, Usami T. Free Oscillation of the Earth. Cambridge University Press. Cambridge. 1981.
  • Referans13. Borg G. Eine Umkehrung der Sturm-Liouvilleschen Eigenwertaufgable. Acta Mathamatica. 78, 1946, 1-96.
  • Referans14. McLaughlin JR. Analytical methods for recovering coefficients in differential equations from spectral data. SIAM. 28(1), 1986, 53-72.
  • Referans15. Hald OH. Discontinuous inverse eigenvalue problems, Communications on Pure and Applied Mathematics. 37(5), 1984, 539-577.
  • Referans16. Yurko VA. On higher-order differantial operators with a singular point. Inverse Problems. 9(4), 1993, 495-502.
  • Referans17. Rundell W, Sacks PE. Reconstruction techniques for classical inverse Sturm-Liouville problems. Math. Comp. 58(197), 1992, 161-183.
  • Referans18. Rundell W, Sacks PE. Reconstruction of a radially symmetric potential from two spectral sequences. J. Math. Anal. Appl. 264(2), 2001, 354-381.
  • Referans19. Yurko VA. Integral transforms connected with discontinuous boundary value problems. Integral Transform. Spec. Funct. 10(2), 2000, 141-164.
  • Referans20. H. Hochstadt H, Lieberman B. An inverse Sturm-Liouville problem with mixed given data. SIAM J. Appl. Math. 34, 1978.
  • Referans21. Hryniv RO, Mykytyuk YV. Half-inverse spectral problems for Sturm-Liouville operators with singular potentials. Inverse Problems. 20(5), 2004, 1423-1444.
  • Referans22. Martinyuk O, Pivovarchik V. On the Hochstadt-Lieberman theorem. Inverse Problems 26(3), 2010, Article ID 035011.
  • Referans23. Sakhnovich L. Half-inverse problems on the finite interval. Inverse Problems. 17(3), 2001, 527-532.
  • Referans24. Ambartsumyan VA. Über eine frage der eigenwerttheorie. Zeitschrift für Physik. 53, 1929, 690-695.
  • Referans25. Xu X-C, Yang C-F. Reconstruction of the Sturm-Liouville operator with discontinuities from a particular set of eigenvalues. Appl. Math. J. Chinese Univ. Ser. B. 33(2), 2018, 225-233.
  • Referans26. Yang C-F. Hochstadt-Lieberman theorem for Dirac operator with eigenparameter dependent boundary conditions. Nonlinear Anal. 74(7), 2011, 2475-2484.
  • Referans27. Koyunbakan H. Inverse problem for a quadratic pencil of Sturm-Liouville operator, J. Math. Anal. Appl. 378, 2011, 549-554.
  • Referans28. Yang C-F, Zettl A. Half inverse problems for quadratic pencils of Stur-Liouville operators. Taiwanese Journal Of Mathematics. 16(5), 2012, 1829-1846.
  • Referans29. Yang C-F, Guo YX. Determination of a differential pencil from interior spectral data. J. Math. Anal. Appl. 375, 2011, 284-293.
  • Referans30. Yang C-F, Yang X-P. An interior inverse problem for the Sturm-Liouville operator with discontinuous conditions. Appl. Math. Lett. 22(9), 2009, 1315-1319.
  • Referans31. Jonas P. On the spectral theory of operators associated with perturbed Klein-Gordon and wave type equations. J. Oper. Theory. 29, 1993, 207-224.
  • Referans32. Keldyshm M. V. On the eigenvalues and eigenfunctions of some classes of nonselffadjoint equations. Dokl. Akad. Nauk SSSR. 77, 1951, 11-14.
  • Referans33. Kostyuchenko AG, Shkalikov AA. Selfadjoint quadratic operator pencils and elliptic problems. Funkc. Anal. Prilozh. 17, 1983, 38-61.
  • Referans34. Marchenko VA. Sturm--Liouville Operators and Their Applications. Naukova Dumka, Kiev (1977). English transl. Birkh\"{a}user. Basel. 1986.
  • Referans35. Yamamoto M. Inverse eigenvalue problem for a vibration of a string with viscous drag. J. Math. Anal. Appl. 152, 1990, 20--34.
Toplam 35 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Volume V Issue III 2020
Yazarlar

Rauf Amirov

Abdullah Ergün 0000-0002-2795-8097

Yayımlanma Tarihi 30 Aralık 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 5 Sayı: 3

Kaynak Göster

APA Amirov, R., & Ergün, A. (2020). Half inverse problems for the impulsive singular diffusion operator. Turkish Journal of Science, 5(3), 186-198.
AMA Amirov R, Ergün A. Half inverse problems for the impulsive singular diffusion operator. TJOS. Aralık 2020;5(3):186-198.
Chicago Amirov, Rauf, ve Abdullah Ergün. “Half Inverse Problems for the Impulsive Singular Diffusion Operator”. Turkish Journal of Science 5, sy. 3 (Aralık 2020): 186-98.
EndNote Amirov R, Ergün A (01 Aralık 2020) Half inverse problems for the impulsive singular diffusion operator. Turkish Journal of Science 5 3 186–198.
IEEE R. Amirov ve A. Ergün, “Half inverse problems for the impulsive singular diffusion operator”, TJOS, c. 5, sy. 3, ss. 186–198, 2020.
ISNAD Amirov, Rauf - Ergün, Abdullah. “Half Inverse Problems for the Impulsive Singular Diffusion Operator”. Turkish Journal of Science 5/3 (Aralık 2020), 186-198.
JAMA Amirov R, Ergün A. Half inverse problems for the impulsive singular diffusion operator. TJOS. 2020;5:186–198.
MLA Amirov, Rauf ve Abdullah Ergün. “Half Inverse Problems for the Impulsive Singular Diffusion Operator”. Turkish Journal of Science, c. 5, sy. 3, 2020, ss. 186-98.
Vancouver Amirov R, Ergün A. Half inverse problems for the impulsive singular diffusion operator. TJOS. 2020;5(3):186-98.
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