Ukrainian Mathematical Journal

, Volume 55, Issue 1, pp 157–163 | Cite as

Multipoint Boundary Conditions for Differential Operators

  • Yu. N. Valitskii
  • B. I. Golets
  • T. I. Zelenyak
Article
  • 16 Downloads

Abstract

We establish differential properties of generalized solutions of multipoint boundary-value problems for ordinary differential equations.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

REFERENCES

  1. 1.
    S. L. Sobolev, Some Applications of Functional Analysis in Mathematical Physics [in Russian], Leningrad University, Leningrad (1950).Google Scholar
  2. 2.
    T. I. Zelenyak, “On one class of boundary-value problems,” in: “Mathematical Models and Methods for Their Investigation” [in Russian], Vol. 1, Krasnoyarsk (2001), pp. 264–267.Google Scholar
  3. 3.
    T. I. Zelenyak and B. I. Golets, “On some boundary-value problems,” in: “Mathematical Models and Methods for Their Investigation” [in Russian], Krasnoyarsk (1999).Google Scholar
  4. 4.
    Yu. N. Valitsky, “Multipoint problem for a differential equation in the Hilbert space,” J. Inver. Ill-Posed Probl., 2, No. 4, 327–347 (1994).Google Scholar
  5. 5.
    S. A. Abdo and N. I. Yurchuk, “Multipoint boundary-value problems for certain differential-operator equations. I. A priori estimates,” Differents. Uravn., 21, No. 3, 417–425 (1985).Google Scholar
  6. 6.
    S. A. Abdo and N. I. Yurchuk, “Multipoint boundary-value problems for certain differential-operator equations. II. Solvability and properties of solutions,” Differents. Uravn., 21, No. 5, 806–815 (1985).Google Scholar
  7. 7.
    T. I. Zelenyak, “On localization of eigenvalues of a spectral problem,” Sib. Mat. Zh., 30, No. 4, 53–61 (1989).Google Scholar
  8. 8.
    Yu. V. Pokornyi, “On some estimates of the Green function of a multipoint boundary-value problem,” Mat. Zametki, 4, No. 6, 533–540 (1968).Google Scholar
  9. 9.
    B. I. Ptashnik, Ill-Posed Boundary-Value Problems for Partial Differential Equations [in Russian], Naukova Dumka, Kiev (1984).Google Scholar
  10. 10.
    A. L. Teptin, “On a multipoint boundary-value problem whose Green function changes its sign in “chess” order,” Differents. Uravn., 20, No. 11, 1910–1911 (1984).Google Scholar
  11. 11.
    F. R. Gantmakher and M. G. Krein, Oscillating Matrices and Kernels and Small Oscillations of Mechanical Systems [in Russian], Gostekhteorizdat, Moscow (1950).Google Scholar
  12. 12.
    M. Sh. Birman, “On the theory of self-adjoint extensions of positive-definite operators,” Mat. Sb., 38 (80), No. 4, 431–450 (1956).Google Scholar
  13. 13.
    K. Friedrichs, “Spektraltheorie halbbeschränkter Operatoren und Anwendung auf die Spektralzerlegung von Differentialoperatoren,” Math. Ann., 109, 465–487 (1934).Google Scholar

Copyright information

© Plenum Publishing Corporation 2003

Authors and Affiliations

  • Yu. N. Valitskii
    • 1
  • B. I. Golets
    • 2
  • T. I. Zelenyak
    • 1
  1. 1.Institute of MathematicsRussian Academy of Sciences, Siberian DivisionNovosibirskRussia
  2. 2.Institute of Economics and Law “Krok,”Kiev

Personalised recommendations