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INTEGRAL REPRESENTATION FOR THE STURM-LIOUVILLE OPERATOR WITH DISCONTINUOUS COEFFICIENT

Year 2015, Volume: 36 Issue: 5, 113 - 133, 28.04.2015
https://doi.org/10.17776/csj.43222

Abstract

In this paper,the Sturm-Liouville with discontinuous coe¢ cient
is considered. ·Integral equations for solution which satisfy certain initial of
given and equation has been obtained and useful integral representation for
Sturm-Liouville operator.

References

  • V.A. Ambartsumyan, Über eine Frage der Eigenwerttheorie, Z. Physik 53 (1929), 690-695.
  • G.Borg, Eine Umkehrung der Sturm-Liouvilleschen Eigenwertaufgabe. Bestimnungder Dif- ferentialgleichung durch die Eigenwerte, Acta Math. 78 (1945), 1-96.
  • N. Levinson, 1949, The Inverse Sturm-Liouville Problem, Mat. Tidsskr. B., pp. 25-30.
  • B. M. Levitan, 1964, Generalized Translation Operators and some of its Applications, Jerusalem.
  • V.A. Marchenko, Some Problems in the Theory of Second-order DiferentialOperators, Dokl. Akad., Nauk SSSR. 72 (1950), 457-560.
  • I. M. Gelfand and B. M. Levitan, 1951 On Determination of a Di¤erentialEquation by its
  • Spectral Function Izv. Akad. Nauk SSSR Ser. Mat. 15 309-60 (in Russian). M.G. Gasimov and B. M. Levitan, About Sturm-Liouville Di¤erential. Operators., Math. Sborn., 63 (105), No. 3, (1964).
  • A.N. Tikhonov, Uniqueness Theorems for Jeophysics Problems, Dokl. Akad. Nauk. SSSR, Vol 69, No 4, 1949, 797-800.
  • R. O. Hryniv and Ya. V. Mykytyuk, Inverse Spectral Problems for Sturm- Liouville Operators with Singular Potentials, Inverse Problems 19 (2003) 665-684.
  • A. M. Savchuk and A. A. Shkalikov, 1999 Sturm-Liouville Operators with Singular Potentials
  • Mat. Zametki 66 897-912 (in Russian). V. A. Marchenko 1950 Some Questions of the Theory of Second Order Dixoerential Operators
  • Dokl. Akad. Nauk SSSR 72 457-60. O. Hald, 1984 Discontinuous Inverse Eigenvalue Problem Commun. Pure Appl. Math. 37 539
  • R. Carlson, 1994 Inverse Sturm-Liouville Problems with a Singularity at Zero Inverse Prob- lems 10 851-64.
  • V. A. Yurko, 2000 Inverse Problems for Di¤erential Equations with Singularities Lying Inside the Interval J. Inverse III-Posed Probl. 8 89-103.
  • R. Kh. Amirov and V. A. Yurko, On Di¤erential Operators with Singularity and Discontinuity Conditions Inside the Interval. Ukr. Math. Jour., 2001, v.53, No11, p. 1443-1458.
  • R. Kh. Amirov, Transformation Operators for Strum-Liouville Operators with Singular Po- tentials, Int. Journal of Pure and Applied Math., 12(3), (2004).
  • R. Kh Amirov, Direct and Inverse Problems for Di¤erential Operators with Singularity and Discontinuity Conditions Inside the Interval Transactions of NASAzerbaijan. R. Kh Amirov, On Sturm-Liouville Operators with Discontinuity Conditions Inside an Inter- val J. Math. Anal. Appl. 317 (2006) 163-176.
  • Nilifer Topsakal, Sonlu Aralıkta Coulomb Potansiyele Sahip Sturm- Liouville Operatörü Için Ters ( Inverse) Problemler (2008)
  • S. Albeverio and P. Kurasov, 2000 Singular Perturbations of Di¤erential Operators, Solvable
  • Schrödinger Type Operators (Cambridge: Cambridge University Press) J. Pöschel and E. Trubowitz, 1987 Inverse Spectral Theory(Pure Appl. Math. Vol 130)(Or- lando, FL:Academic).
Year 2015, Volume: 36 Issue: 5, 113 - 133, 28.04.2015
https://doi.org/10.17776/csj.43222

Abstract

References

  • V.A. Ambartsumyan, Über eine Frage der Eigenwerttheorie, Z. Physik 53 (1929), 690-695.
  • G.Borg, Eine Umkehrung der Sturm-Liouvilleschen Eigenwertaufgabe. Bestimnungder Dif- ferentialgleichung durch die Eigenwerte, Acta Math. 78 (1945), 1-96.
  • N. Levinson, 1949, The Inverse Sturm-Liouville Problem, Mat. Tidsskr. B., pp. 25-30.
  • B. M. Levitan, 1964, Generalized Translation Operators and some of its Applications, Jerusalem.
  • V.A. Marchenko, Some Problems in the Theory of Second-order DiferentialOperators, Dokl. Akad., Nauk SSSR. 72 (1950), 457-560.
  • I. M. Gelfand and B. M. Levitan, 1951 On Determination of a Di¤erentialEquation by its
  • Spectral Function Izv. Akad. Nauk SSSR Ser. Mat. 15 309-60 (in Russian). M.G. Gasimov and B. M. Levitan, About Sturm-Liouville Di¤erential. Operators., Math. Sborn., 63 (105), No. 3, (1964).
  • A.N. Tikhonov, Uniqueness Theorems for Jeophysics Problems, Dokl. Akad. Nauk. SSSR, Vol 69, No 4, 1949, 797-800.
  • R. O. Hryniv and Ya. V. Mykytyuk, Inverse Spectral Problems for Sturm- Liouville Operators with Singular Potentials, Inverse Problems 19 (2003) 665-684.
  • A. M. Savchuk and A. A. Shkalikov, 1999 Sturm-Liouville Operators with Singular Potentials
  • Mat. Zametki 66 897-912 (in Russian). V. A. Marchenko 1950 Some Questions of the Theory of Second Order Dixoerential Operators
  • Dokl. Akad. Nauk SSSR 72 457-60. O. Hald, 1984 Discontinuous Inverse Eigenvalue Problem Commun. Pure Appl. Math. 37 539
  • R. Carlson, 1994 Inverse Sturm-Liouville Problems with a Singularity at Zero Inverse Prob- lems 10 851-64.
  • V. A. Yurko, 2000 Inverse Problems for Di¤erential Equations with Singularities Lying Inside the Interval J. Inverse III-Posed Probl. 8 89-103.
  • R. Kh. Amirov and V. A. Yurko, On Di¤erential Operators with Singularity and Discontinuity Conditions Inside the Interval. Ukr. Math. Jour., 2001, v.53, No11, p. 1443-1458.
  • R. Kh. Amirov, Transformation Operators for Strum-Liouville Operators with Singular Po- tentials, Int. Journal of Pure and Applied Math., 12(3), (2004).
  • R. Kh Amirov, Direct and Inverse Problems for Di¤erential Operators with Singularity and Discontinuity Conditions Inside the Interval Transactions of NASAzerbaijan. R. Kh Amirov, On Sturm-Liouville Operators with Discontinuity Conditions Inside an Inter- val J. Math. Anal. Appl. 317 (2006) 163-176.
  • Nilifer Topsakal, Sonlu Aralıkta Coulomb Potansiyele Sahip Sturm- Liouville Operatörü Için Ters ( Inverse) Problemler (2008)
  • S. Albeverio and P. Kurasov, 2000 Singular Perturbations of Di¤erential Operators, Solvable
  • Schrödinger Type Operators (Cambridge: Cambridge University Press) J. Pöschel and E. Trubowitz, 1987 Inverse Spectral Theory(Pure Appl. Math. Vol 130)(Or- lando, FL:Academic).
There are 20 citations in total.

Details

Primary Language English
Journal Section Natural Sciences Research Article
Authors

Rauf Amirov

Sevim Durak

Publication Date April 28, 2015
Published in Issue Year 2015 Volume: 36 Issue: 5

Cite

APA Amirov, R., & Durak, S. (2015). INTEGRAL REPRESENTATION FOR THE STURM-LIOUVILLE OPERATOR WITH DISCONTINUOUS COEFFICIENT. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi, 36(5), 113-133. https://doi.org/10.17776/csj.43222
AMA Amirov R, Durak S. INTEGRAL REPRESENTATION FOR THE STURM-LIOUVILLE OPERATOR WITH DISCONTINUOUS COEFFICIENT. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi. August 2015;36(5):113-133. doi:10.17776/csj.43222
Chicago Amirov, Rauf, and Sevim Durak. “INTEGRAL REPRESENTATION FOR THE STURM-LIOUVILLE OPERATOR WITH DISCONTINUOUS COEFFICIENT”. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi 36, no. 5 (August 2015): 113-33. https://doi.org/10.17776/csj.43222.
EndNote Amirov R, Durak S (August 1, 2015) INTEGRAL REPRESENTATION FOR THE STURM-LIOUVILLE OPERATOR WITH DISCONTINUOUS COEFFICIENT. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi 36 5 113–133.
IEEE R. Amirov and S. Durak, “INTEGRAL REPRESENTATION FOR THE STURM-LIOUVILLE OPERATOR WITH DISCONTINUOUS COEFFICIENT”, Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi, vol. 36, no. 5, pp. 113–133, 2015, doi: 10.17776/csj.43222.
ISNAD Amirov, Rauf - Durak, Sevim. “INTEGRAL REPRESENTATION FOR THE STURM-LIOUVILLE OPERATOR WITH DISCONTINUOUS COEFFICIENT”. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi 36/5 (August 2015), 113-133. https://doi.org/10.17776/csj.43222.
JAMA Amirov R, Durak S. INTEGRAL REPRESENTATION FOR THE STURM-LIOUVILLE OPERATOR WITH DISCONTINUOUS COEFFICIENT. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi. 2015;36:113–133.
MLA Amirov, Rauf and Sevim Durak. “INTEGRAL REPRESENTATION FOR THE STURM-LIOUVILLE OPERATOR WITH DISCONTINUOUS COEFFICIENT”. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi, vol. 36, no. 5, 2015, pp. 113-3, doi:10.17776/csj.43222.
Vancouver Amirov R, Durak S. INTEGRAL REPRESENTATION FOR THE STURM-LIOUVILLE OPERATOR WITH DISCONTINUOUS COEFFICIENT. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi. 2015;36(5):113-3.