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Mat. Sb., 2007, Volume 198, Number 11, Pages 47–66 (Mi msb1491)  

This article is cited in 32 scientific papers (total in 32 papers)

The inverse spectral problem for pencils of differential operators

I. M. Guseinovab, I. M. Nabievab

a Baku State University
b Institute of Mathematics and Mechanics, Azerbaijan National Academy of Sciences

Abstract: The inverse problem of spectral analysis for a quadratic pencil of Sturm–Liouville operators on a finite interval is considered. A uniqueness theorem is proved, a solution algorithm is presented, and sufficient conditions for the solubility of the inverse problem are obtained.
Bibliography: 31 titles.


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English version:
Sbornik: Mathematics, 2007, 198:11, 1579–1598

Bibliographic databases:

UDC: 517.984
MSC: Primary 34B24, 34L05; Secondary 47E05
Received: 11.01.2006 and 11.04.2007

Citation: I. M. Guseinov, I. M. Nabiev, “The inverse spectral problem for pencils of differential operators”, Mat. Sb., 198:11 (2007), 47–66; Sb. Math., 198:11 (2007), 1579–1598

Citation in format AMSBIB
\by I.~M.~Guseinov, I.~M.~Nabiev
\paper The inverse spectral problem for pencils
of differential operators
\jour Mat. Sb.
\yr 2007
\vol 198
\issue 11
\pages 47--66
\jour Sb. Math.
\yr 2007
\vol 198
\issue 11
\pages 1579--1598

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    This publication is cited in the following articles:
    1. I. M. Nabiev, A. Sh. Shukyurov, “Reshenie obratnoi zadachi dlya operatora diffuzii v simmetrichnom sluchae”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 9:4(1) (2009), 36–40  mathnet  elib
    2. Yang Chuan Fu, “New trace formulae for a quadratic pencil of the Schrödinger operator”, J. Math. Phys., 51:3 (2010), 033506, 10 pp.  crossref  mathscinet  zmath  adsnasa  isi  scopus
    3. Yang Chuan-Fu, Yang Xiao-Ping, “Inverse nodal problems for differential pencils on a star-shaped graph”, Inverse Probl., 26:8 (2010), 085008, 15 pp.  crossref  mathscinet  zmath  adsnasa  isi  scopus
    4. Chuan Fu Yang, Zhen You Huang, Yu Ping Wang, “Trace formulae for the Schrödinger equation with energy-dependent potential”, J. Phys. A, 43:41 (2010), 415207, 15 pp.  crossref  mathscinet  zmath  isi  scopus
    5. A. M. Akhtyamov, V. A. Sadovnichy, Ya. T. Sultanaev, “Inverse problem for an operator pencil with nonseparated boundary conditions”, Eurasian Math. J., 1:2 (2010), 5–16  mathnet  mathscinet  zmath
    6. Koyunbakan H., “Inverse problem for a quadratic pencil of Sturm-Liouville operator”, J. Math. Anal. Appl., 378:2 (2011), 549–554  crossref  mathscinet  zmath  isi  scopus
    7. I. M. Nabiev, “Solution of the Inverse Quasiperiodic Problem for the Dirac System”, Math. Notes, 89:6 (2011), 845–852  mathnet  crossref  crossref  mathscinet  isi
    8. Hryniv R., Pronska N., “Inverse spectral problems for energy-dependent Sturm-Liouville equations”, Inverse Probl., 28:8 (2012), 08500  crossref  mathscinet  isi  elib  scopus
    9. Sadovnichii V.A. Sultanaev Ya.T. Akhtyamov A.M., “Generalization of B. M. Levitan and M. G. Gasymov's solvability theorems to the case of indecomposable boundary conditions”, Dokl. Math., 85:2 (2012), 289–291  crossref  mathscinet  zmath  isi  elib  elib  scopus
    10. A. M. Akhtyamov, V. A. Sadovnichy, Ya. T. Sultanaev, “Generalizations of Borg's uniqueness theorem to the case of nonseparated boundary conditions”, Eurasian Math. J., 3:4 (2012), 10–22  mathnet  mathscinet  zmath
    11. Chuan-Fu Yang, “Trace formulae for differential pencils with spectral parameter dependent boundary conditions”, Math. Meth. Appl. Sci, 2013, n/a  crossref  mathscinet  scopus
    12. Manafov M.D., Kablan A., “Inverse Scattering Problems for Energy-Dependent Sturm-Liouville Equations with Point Delta-Interaction and Eigenparameter-Dependent Boundary Condition”, Electron. J. Differ. Equ., 2013, 237  mathscinet  zmath  isi
    13. Pronska N., “Reconstruction of Energy-Dependent Sturm-Liouville Equations From Two Spectra”, Integr. Equ. Oper. Theory, 76:3 (2013), 403–419  crossref  mathscinet  zmath  isi  elib  scopus
    14. Manafov M.D., “Half-Inverse Spectral Problem for Differential Pencils with Interaction-Point and Eigenvalue-Dependent Boundary Conditions”, Hacet. J. Math. Stat., 42:4 (2013), 339–345  mathscinet  zmath  isi
    15. Chuan-Fu Yang, “On the quasinodal map for the diffusion operator”, Journal of Functional Analysis, 2014  crossref  mathscinet  isi  scopus
    16. G. Freiling, V. Yurko, “Recovering nonselfadjoint differential pencils with nonseparated boundary conditions”, Applicable Analysis, 2014, 1  crossref  mathscinet  scopus
    17. V. A. Sadovnichii, Ya. T. Sultanaev, A. M. Akhtyamov, “A generalization of Borg’s uniqueness theorems for a symmetric potential to general boundary conditions”, Dokl. Math, 90:2 (2014), 565  crossref  mathscinet  zmath  elib  scopus
    18. Sadovnichii V.A., Sultanaev Ya.T., Akhtyamov A.M., “A Generalization of Levinson's Uniqueness Theorem To the Case of General Boundary Conditions”, Dokl. Math., 90:3 (2014), 715–718  crossref  mathscinet  zmath  isi  elib  scopus
    19. Guseinov I.M., Mammadova L.I., “Reconstruction of the Diffusion Equation With Singular Coefficients For Two Spectra”, Dokl. Math., 90:1 (2014), 401–404  crossref  mathscinet  zmath  isi  elib  scopus
    20. Nabiev I.M., “Determination of the Diffusion Operator on An Interval”, Colloq. Math., 134:2 (2014), 165–178  crossref  mathscinet  zmath  isi  elib  scopus
    21. Manafov Manaf D. Z. H., Kablan A., “Inverse Spectral and Inverse Nodal Problems For Energy-Dependent Sturm-Liouvillee Quations With Delta-Interaction”, Electron. J. Differ. Equ., 2015, 26  mathscinet  zmath  isi  elib
    22. Sadovnichii V.A., Sultanaev Ya.T., Akhtyamov A.M., “General Inverse Sturm-Liouville Problem With Symmetric Potential”, Azerbaijan J. Math., 5:2 (2015), 96–108  mathscinet  zmath  isi  elib
    23. Sadovnichii V.A., Sultanaev Ya.T., Akhtyamov A.M., “Solvability Theorems For An Inverse Nonself-Adjoint Sturm-Liouville Problem With Nonseparated Boundary Conditions”, Differ. Equ., 51:6 (2015), 717–725  crossref  mathscinet  zmath  isi  scopus
    24. Guo Y., Wei G., “Inverse Problem For Differential Pencils With Incompletely Spectral Information”, Taiwan. J. Math., 19:3 (2015), 927–942  crossref  mathscinet  zmath  isi  elib  scopus
    25. T. Sh. Abdullaev, I. M. Nabiev, “An algorithm for reconstructing the Dirac operator with a spectral parameter in the boundary condition”, Comput. Math. Math. Phys., 56:2 (2016), 256–262  mathnet  crossref  crossref  isi  elib
    26. Yurko V., “Inverse Problem for Quasi-Periodic Differential Pencils with Jump Conditions Inside the Interval”, Complex Anal. Oper. Theory, 10:6 (2016), 1203–1212  crossref  mathscinet  zmath  isi  scopus
    27. Ibadzadeh Ch.G., Nabiev I.M., “An inverse problem for Sturm–Liouville operators with non-separated boundary conditions containing the spectral parameter”, J. Inverse Ill-Posed Probl., 24:4 (2016), 407–411  crossref  mathscinet  zmath  isi  scopus
    28. Manafov M.D., “Inverse spectral problems for energy-dependent Sturm-Liouville equations with -interaction”, Filomat, 30:11 (2016), 2935–2946  crossref  mathscinet  zmath  isi  elib  scopus
    29. A. M. Akhtyamov, V. A. Sadovnichy, Ya. T. Sultanaev, “Inverse problem for the diffusion operator with symmetric functions and general boundary conditions”, Eurasian Math. J., 8:1 (2017), 10–22  mathnet
    30. Akhtyamov A.M., “Degenerate Boundary Conditions For the Diffusion Operator”, Differ. Equ., 53:11 (2017), 1515–1518  crossref  mathscinet  zmath  isi
    31. Gulsen T., Sian Shaida Saber Mawlood, Yilmaz E., Koyunbakan H., “Impulsive Diffusion Equation on Time Scales”, Int. J. Anal. Appl., 16:1 (2018), 137–148  crossref  zmath  isi  scopus
    32. Gulsen T., Panakhov E.S., “On the Isospectrality of the Scalar Energy-Dependent Schrodinger Problems”, Turk. J. Math., 42:1 (2018), 139–154  crossref  mathscinet  isi
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