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Siberian Mathematical Journal

, Volume 44, Issue 5, pp 813–816 | Cite as

On the Basis Properties of One Spectral Problem with a Spectral Parameter in a Boundary Condition

  • N. B. Kerimov
  • V. S. Mirzoev
Article

Abstract

We consider a second-order ordinary differential operator with the same spectral parameter in the equation and in one of the boundary conditions. We study the basis property of the system of eigenfunctions of this operator in the space of square summable functions.

ordinary differential operator oscillation eigenfunction biorthogonal system basis 

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References

  1. 1.
    Walter J., “Regular eigenvalue problems with eigenvalue parameter in the boundary condition,” Math. Z., 133, No. 4, 301–312 (1973).Google Scholar
  2. 2.
    Schneider A., “A note on eigenvalue problems, with eigenvalue parameter in the boundary conditions,” Math. Z., 136, No. 2, 163–167 (1974).Google Scholar
  3. 3.
    Fulton C. T., “Two-point boundary value problems with eigenvalue parameter contained in the boundary conditions,” Proc. Roy. Soc. Edinburgh Sect. A, 77, 293–388 (1977).Google Scholar
  4. 4.
    Hinton D. B., “An expansion theorem for an eigenvalue problem with eigenvalue parameter in the boundary condition,” Quart. J. Math. Oxford Ser. (2), 30, No. 2, 33–42 (1979).Google Scholar
  5. 5.
    Shkalikov A. A., “Boundary value problems for ordinary differential equations with a parameter in the boundary conditions,” Trudy Sem. Petrovsk., No. 9, 190–229 (1983).Google Scholar
  6. 6.
    Kerimov N. B. and Allakhverdiev T. I., “On a certain boundary value problem. I,” Differentsial'nye Uravneniya, 29, No. 1, 54–60 (1993).Google Scholar
  7. 7.
    Kerimov N. B. and Allakhverdiev T. I., “On a certain boundary value problem. II,” Differentsial'nye Uravneniya, 29, No. 6, 952–960 (1993).Google Scholar
  8. 8.
    Binding P. A., Browne P. J., and Seddighi K., “Sturm-Lioville problems with eigenparameter dependent boundary conditions,” Proc. Edinburgh Math. Soc. (2), 37, No. 1, 57–72 (1993).Google Scholar
  9. 9.
    Kapustin N. Yu. and Moiseev E. I., “On the spectral problem from the theory of the parabolic-hyperbolic heat equation,” Dokl. Ross. Akad. Nauk, 352, No. 4, 451–454 (1997).Google Scholar
  10. 10.
    Kapustin N. Yu. and Moiseev E. I., “Spectral problems with the spectral parameter in the boundary condition,” Differentsial'nye Uravneniya, 33, No. 1, 115–119 (1997).Google Scholar
  11. 11.
    Kerimov N. B. and Mamedov Kh. R., “On one boundary value problem with a spectral parameter in the boundary conditions,” Sibirsk. Mat. Zh., 40, No. 2, 325–335 (1999).Google Scholar
  12. 12.
    Kapustin N. Yu., “Oscillation properties of solutions to a nonselfadjoint spectral problem with spectral parameter in the boundary condition,” Differentsial'nye Uravneniya, 35, No. 8, 1024–1027 (1999).Google Scholar
  13. 13.
    Na?mark M. A., Linear Differential Operators [in Russian], Nauka, Moscow (1969).Google Scholar

Copyright information

© Plenum Publishing Corporation 2003

Authors and Affiliations

  • N. B. Kerimov
    • 1
  • V. S. Mirzoev
    • 2
  1. 1.Baku State UniversityAzerbaijan
  2. 2.Institute of Mathematics and MechanicsBaku

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