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Mat. Sb., 2000, Volume 191, Number 10, Pages 137–160 (Mi msb520)  

This article is cited in 47 scientific papers (total in 47 papers)

An inverse problem for differential operator pencils

V. A. Yurko

Saratov State University named after N. G. Chernyshevsky

Abstract: An inverse spectral problem of recovering a second-order differential operator pencil on the half-line is investigated. A uniqueness theorem is proved; necessary and sufficient conditions for the solubility, and an algorithm for the solution of the inverse problem are obtained. Relations with inverse problems for partial differential equations are pointed out.

DOI: https://doi.org/10.4213/sm520

Full text: PDF file (316 kB)
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English version:
Sbornik: Mathematics, 2000, 191:10, 1561–1586

Bibliographic databases:

UDC: 517.984
MSC: 34B24, 34L99, 34A55, 35L05, 35R30
Received: 22.11.1999

Citation: V. A. Yurko, “An inverse problem for differential operator pencils”, Mat. Sb., 191:10 (2000), 137–160; Sb. Math., 191:10 (2000), 1561–1586

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. A. Yurko, “An inverse spectral problem for singular non-self-adjoint differential systems”, Sb. Math., 195:12 (2004), 1823–1854  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. Yurko V.A., “An inverse problem for differential systems on a finite interval in the case of multiple roots of the characteristic polynomial”, Differ. Equ., 41:6 (2005), 818–823  mathnet  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    3. V. A. Yurko, “Recovering singular differential pencils with a turning point”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 5:1-2 (2005), 71–81  mathnet
    4. V. A. Yurko, “The inverse problem for pencils of differential operators on the half-line with turning points”, J. Math. Sci., 150:6 (2008), 2620–2627  mathnet  crossref  mathscinet  zmath  elib  elib
    5. Yurko V., “Inverse spectral problems for differential pencils on the half-line with turning points”, J. Math. Anal. Appl., 320:1 (2006), 439–463  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    6. I. M. Guseinov, I. M. Nabiev, “The inverse spectral problem for pencils of differential operators”, Sb. Math., 198:11 (2007), 1579–1598  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    7. Mamedov K.R., “On the inverse problem for Sturm-Liouville operator with a nonlinear spectral parameter in the boundary condition”, J. Korean Math. Soc., 46:6 (2009), 1243–1254  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    8. Chernozhukova A., Freiling G., “A uniqueness theorem for the boundary value problems with non-linear dependence on the spectral parameter in the boundary conditions”, Inverse Probl. Sci. Eng., 17:6 (2009), 777–785  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    9. Buterin S.A., Shieh Chung Tsun, “Inverse nodal problem for differential pencils”, Appl. Math. Lett., 22:8 (2009), 1240–1247  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    10. Mamedov Kh.R., Menken H., “The Levinson-type formula for a boundary value problem with a spectral parameter in the boundary condition”, Arab. J. Sci. Eng. Sect. A Sci., 34:1 (2009), 219–226  mathscinet  zmath  isi
    11. 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
    12. 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
    13. Mamedov Kh.R., “On an Inverse Scattering Problem for a Discontinuous Sturm-Liouville Equation with a Spectral Parameter in the Boundary Condition”, Bound Value Probl., 2010, 171967, 17 pp.  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    14. Mamedov Kh.R., Kosar A.P., “Inverse scattering problem for Sturm-Liouville operator with nonlinear dependence on the spectral parameter in the boundary condition”, Math Methods Appl Sci, 34:2 (2011), 231–241  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus  scopus
    15. Aynur Çöl, Kh.R. Mamedov, “On an inverse scattering problem for a class of Dirac operators with spectral parameter in the boundary condition”, Journal of Mathematical Analysis and Applications, 2012  crossref  mathscinet  isi  scopus  scopus  scopus
    16. A. Neamaty, Y. Khalili, “The differential pencils with turning point on the half line”, Arab Journal of Mathematical Sciences, 2012  crossref  mathscinet
    17. Buterin S.A., Yurko V.A., “Inverse Problems for Second-Order Differential Pencils with Dirichlet Boundary Conditions”, J. Inverse Ill-Posed Probl., 20:5-6 (2012), 855–881  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    18. Buterin S.A., Shieh C.-T., “Incomplete Inverse Spectral and Nodal Problems for Differential Pencils”, Results Math., 62:1-2 (2012), 167–179  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    19. Ozkan A.S., “Inverse Sturm-Liouville Problems with Eigenvalue-Dependent Boundary and Discontinuity Conditions”, Inverse Probl. Sci. Eng., 20:6 (2012), 857–868  crossref  mathscinet  isi  elib  scopus  scopus  scopus
    20. Amirov R.Kh. Nabiev A.A., “Inverse Problems for the Quadratic Pencil of the Sturm-Liouville Equations with Impulse”, Abstract Appl. Anal., 2013, 361989  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    21. A. Cabada, A. Yakhshimuratov, “The System of Kaup Equations with a Self-Consistent Source in the Class of Periodic Functions”, Zhurn. matem. fiz., anal., geom., 9:3 (2013), 287–303  mathnet  mathscinet
    22. N. P. Bondarenko, “An inverse problem for the matrix quadratic pencil on a finite interval”, Eurasian Math. J., 4:3 (2013), 20–31  mathnet
    23. Yang Ch.-F., “Uniqueness Theorems for Differential Pencils with Eigenparameter Boundary Conditions and Transmission Conditions”, J. Differ. Equ., 255:9 (2013), 2615–2635  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus  scopus
    24. 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
    25. 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
    26. Karaman O., Kosar N.P., “Continuity of the Scattering Function and Levinson-Type Formula of Klein-Gordon Equation”, Math. Meth. Appl. Sci., 36:12 (2013), 1583–1590  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    27. Neamaty A., Khalili Y., “The Uniqueness Theorem For Differential Pencils With the Jump Condition in the Finite Interval”, Iran. J. Sci. Technol. Trans. A-Sci., 38:A3, SI (2014), 305–309  mathscinet  isi
    28. Sat M., Panakhov E.S., “Inverse Problem For Diffusion Operators on the Finite Interval”, 10th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences, AIP Conference Proceedings, 1637, ed. Sivasundaram S., Amer Inst Physics, 2014, 968–975  crossref  isi  scopus  scopus
    29. Cakmak Ya., Isik S., “Recovery of the Impulsive Diffusion Operator With Discontinuous Coefficient”, Appl. Math. Inf. Sci., 8:5 (2014), 2267–2275  crossref  mathscinet  isi  elib  scopus  scopus  scopus
    30. Bondarenko N., Freiling G., “An Inverse Problem For the Quadratic Pencil of Non-Self-Adjoint Matrix Operators on the Half-Line”, J. Inverse Ill-Posed Probl., 22:4 (2014), 467–495  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    31. Sat M., Panakhov E.S., “Spectral Problem For Diffusion Operator”, Appl. Anal., 93:6 (2014), 1178–1186  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    32. Yang Ch.-F., Yu X.-J., “Determination of Differential Pencils With Spectral Parameter Dependent Boundary Conditions From Interior Spectral Data”, Math. Meth. Appl. Sci., 37:6 (2014), 860–869  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    33. Ozkan A.S., “Half-Inverse Sturm-Liouville Problem With Boundary and Discontinuity Conditions Dependent on the Spectral Parameter”, Inverse Probl. Sci. Eng., 22:5 (2014), 848–859  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    34. Nabiev I.M., “Determination of the Diffusion Operator on An Interval”, Colloq. Math., 134:2 (2014), 165–178  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    35. 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
    36. 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  scopus  scopus
    37. Col A., “Inverse Spectral Problem For Sturm-Liouville Operator With Discontinuous Coefficient and Cubic Polynomials of Spectral Parameter in Boundary Condition”, Adv. Differ. Equ., 2015, 132  crossref  mathscinet  isi  elib  scopus  scopus  scopus
    38. Manafov M.D., “Inverse Spectral Problems For Energy-Dependent Sturm-Liouville Equations With Finitely Many Point Delta-Interactions”, Electron. J. Differ. Equ., 2016, 11  mathscinet  zmath  isi
    39. Bondarenko N., “Recovery of the matrix quadratic differential pencil from the spectral data”, J. Inverse Ill-Posed Probl., 24:3 (2016), 245–263  crossref  mathscinet  zmath  isi  scopus
    40. Cakmak Ya., Isik S., “Half inverse problem for the impulsive diffusion operator with discontinuous coefficient”, Filomat, 30:1 (2016), 157–168  crossref  mathscinet  zmath  isi  scopus
    41. 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
    42. 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
    43. Xu X.-Ch., Yang Ch.-F., You H.-Zh., “Inverse Spectral Analysis For Regge Problem With Partial Information on the Potential”, Results Math., 71:3-4 (2017), 983–996  crossref  mathscinet  zmath  isi  scopus
    44. Mizrak O., Mamedov Kh.R., Akhtyamov A.M., “Characteristic Properties of Scattering Data of a Boundary Value Problem”, Filomat, 31:12 (2017), 3945–3951  crossref  mathscinet  isi  scopus  scopus  scopus
    45. Ying Yang, Guangsheng Wei, “Inverse Scattering Problems for Sturm–Liouville Operators with Spectral Parameter Dependent on Boundary Conditions”, Math. Notes, 103:1 (2018), 59–66  mathnet  crossref  crossref  isi  elib
    46. 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  scopus  scopus  scopus
    47. Yang Ch.-F., Yurko V., “On the Determination of Differential Pencils With Nonlocal Conditions”, J. Inverse Ill-Posed Probl., 26:5 (2018), 577–588  crossref  mathscinet  zmath  isi  scopus
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