Skip to main content
SpringerLink
Log in

Linear Noetherian boundary value problems for differential systems with an impulse action

  • Brief Communications
  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

A solvability criterion of linear nonhomogeneous boundary value problems is obtained for systems of ordinary differential equations with impulse action in the general case when the number of boundary conditions does not coincide with the order of the differential system (Noetherian problems). The generalized Green operator of such boundary value problems is constructed. Its connection with the generalized inverse operator of the operator of the original boundary value problem is shown.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Literature cited

  1. A. M. Samoilenko and N. A. Perestyuk, Differential Equations with Impulse Action [in Russian], Vishcha Shkola, Kiev (1987).

    Google Scholar 

  2. S. T. Zavalishchin, A. N. Sesekin, and S. E. Drozdenko, Dynamical Systems with Impulse Structure [in Russian], Sred. Ural. Kn. Izd., Sverdlovsk (1983).

    Google Scholar 

  3. A. Khalanai (A. Halanay) and D. Veksler (D. Wexler), The Qualitative Theory of Systems with Impulses [Russian translation], Mir, Moscow (1971).

    Google Scholar 

  4. A. A. Boichuk, Constructive Methods in the Analysis of Boundary Value Problems [in Russian], Naukova Dumka, Kiev (1990).

    Google Scholar 

  5. M. Z. Nashed (ed.), Generalized Inverses and Applications, Academic Press, New York (1976).

    Google Scholar 

  6. V. P. Maksimov, “The Noetherian property of the general boundary value problem for a linear functional differential equation,” Differents. Uravn.,10, No. 12, 2288–2291 (1974).

    Google Scholar 

  7. A. A. Boichuk and V. F. Zhuravlev, “The construction of solutions of linear Noetherian operator equations in a Hilbert space,” Dokl. Akad. Nauk UkrSSR, Ser. A, No. 8, 6–9 (1990).

    Google Scholar 

  8. A. Bojchuk and V. Juravliov, “Generalized inverses for Noether's operators in Banach spaces,” in: Fifth Conference on Numerical Methods, Hungary (1990), p. 11.

  9. L. F. Rakhmatullina, “On the regularization of linear boundary value problems,” Izv. Vyssh. Uchebn. Zaved. Matem., No. 7, 37–43 (1987).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, Academy of Sciences of the Ukraine, Kiev

    A. M. Samoilenko & A. A. Boichuk

  2. Institute of Geophysics, Academy of Sciences of the Ukraine, Kiev

    A. M. Samoilenko & A. A. Boichuk

Authors
  1. A. M. Samoilenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. A. Boichuk
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 4, pp. 564–568, April, 1992.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Samoilenko, A.M., Boichuk, A.A. Linear Noetherian boundary value problems for differential systems with an impulse action. Ukr Math J 44, 504–508 (1992). https://doi.org/10.1007/BF01064886

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01064886

Keywords

Search

Navigation