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ON A DIRECT PROBLEM OF SCATTERING THEORY FOR A CLASS OF STURM-LIOUVILLE OPERATOR WITH DISCONTINOUS COEFFICIENT

Mamedov|Palamut
장전수학회 (Jangjeon Mathematical Society)|2009.10|Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집) (Proceedings of the Jangjeon Mathematical Society)|제12권 제2호|pp. 243-251|DOI 10.17777/pjms.2009.12.2.011

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참고문헌

키워드

The expansion formularesolventdiscontinous boundary-value prob- lemSturm-Liouville operator.
주제분류수학

초록

In this paper we consider a second order di¤erential equation with a discontinuous coe¢ cient and spectral parameter dependent boundary con- dition in the half line. The operator interpretation of the given boundary value problem is investigated in the Hilbert space [수식]. The resolvent operator is constructed and the expansion formula with respect to eigenfunctions is obtained.

Abstract

In this paper we consider a second order di¤erential equation with a discontinuous coe¢ cient and spectral parameter dependent boundary con- dition in the half line. The operator interpretation of the given boundary value problem is investigated in the Hilbert space [수식]. The resolvent operator is constructed and the expansion formula with respect to eigenfunctions is obtained.

참고문헌 (14)

  1. C. T. Fulton, "Two-point Boundary Value Problems with Eigenvalue Parameter Contained in the Boundary Conditions", Proc. Roy. Soc. Edin., 77A, pp.293~308 (1977)
  2. C. T. Fulton, "Two-Point Boundary-Value Problems with Eigenvalues Parameter Contained in the Boundary Conditions", Proc. Roy. Soc. Edingburgh, 77A, pp.293~308 (1977)
  3. E. M Russakovskij, "An Operator Interpretation of the Boundary Value Problem with a Polynomial Spectral Parameter in the Boundary Conditions", Fun. Analysis and Its Ap- plications, 9, pp.91~92 (1975)
  4. N. Yu. Kapustin, "On a Spectral Problems with Spectral Parameters in Bound- ary Condition", Di¤ . Equation,, 33, pp.115~119 (1997)
  5. Kh. R. Mamedov, "On the Inverse Problem of Scattering Theory for a Differential Operator of the Second Order", Functional Analysis and its Applications, North - Holland Mathematics Studies, 197, pp.185~194 (2004)
  6. N. B. Kerimov, "On Basis Properties of One Spectral Problem with Spectral Parameters in Boundary Condition", Sib. Math. Journ, 44, pp.1041~1045 (2003)
  7. V. A. Marchenko, "Sturm-Liouville Operators and their Applications", Basel- Birkhauser, ~ (1986)
  8. Kh. R. Mamedov, "On One Boundary Value Problem with Parameter in Boundary Conditions", Spectral Theory of Operators and Its Applications, XI, pp.117~121 (1997)
  9. V.Y. Gulmamedov, "On Basis Property for a Boundary-Value Problem with Spectral Parameter in the Boundary Condition", Journal of Arts and Science, (5), pp.9~17 (2006), Çankaya University
  10. Kh. R. Mamedov, "On a Basis Problem for a Second Order Di¤erential Equation with a Discontinuous Coe¢ cient and a Spectral Parameter in the Boundary Conditions", pp.218~225 (2005), Geom- etry,Integrability and Quantization
  11. Kh. R. Mamedov, "Uniqueness of the Solution to the Inverse Problem of Scattering Theory for the Sturm-Liouville Operator with a Spectral Parameter in the Boundary Condition", Math. Notes, 74(1), pp.136~140 (2003)
  12. Kh. R. Mamedov, "Uniqueness of the Solution of the Inverse Problem of Scattering Theory for Sturm-Liouville Operator with Discontinuous Coe¢ cient", Proceedings of IMM of NAS Azerbaijan, 24, pp.263~272 (2006)
  13. I. M. Guseinov, "On a Inverse Problem for a Second Order Di¤erential Equation", Usp. Math. Nauk, 57(3), pp.597~598 (2002)
  14. E. C. Titchmarsh, "Eigenfunction Expansions", ~ (1962)

관련 논문AI추천

On a spectral expansion formula for a class of second order differential equation with discontinuous coefficientF. A. Cetinkaya, Kh. R. Mamedov장전수학회 · Advanced Studies in Contemporary Mathematics2014 · 제24권 제4호On the inverse problem for Sturm-Liouville operator with a nonlinear spectral parameter in the boundary conditionKhanlar R. Mamedov대한수학회 · 대한수학회지2009 · 제46권 제6호THE REGULARIZED TRACE FORMULA FOR A DIFFERENTIAL OPERATOR WITH UNBOUNDED OPERATOR COEFFICIENTA. Bayramov, E. Şen, K. Oruçoğlu장전수학회 · Advanced Studies in Contemporary Mathematics2015 · 제25권 제4호Uniqueness of the solution of half inverse problem for the impulsive Sturm Liouville operatorA. Sinan Ozkan, Baki Keskin, Yasar Cakmak대한수학회 · 대한수학회보2013 · 제50권 제2호Comparative Analysis of Spectral Theory of Second Order Difference and Differential Operators with Unbounded Odd CoefficientDavid Otieno Ambogo, Fredrick Oluoch Nyamwala, Joyce Mukhwana Ngala경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2020 · 제60권 제2호Spectral Analysis of Four Term Differential OperatorNyamwala Fredrick Oluoch경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2010 · 제50권 제1호

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