Skip to main content
SpringerLink
Log in

Weakly nonlinear boundary-value problems for differential systems with pulse influence

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

The coefficient sufficient conditions for the existence of solutions and the iteration algorithm of constructing these solutions are obtained for weakly nonlinear boundary-value problems for systems of ordinary differential equations with pulse influence in the general case in which the number of boundary conditions does not coincide with the order of the differential system. The equation is derived for generating amplitudes of these boundary-value problems. This equation determines the amplitude of a solution, which can be regarded as generating for the required solution, and gives necessary conditions for the existence of this solution.

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

Similar content being viewed by others

References

  1. A. M. Samoilenko and N. A. Perestyuk,Differential Equations with Pulse Influence [in Russian], Vyshcha Shkola, Kiev (1987).

    Google Scholar 

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

    Google Scholar 

  3. A. M. Samoilenko and A. A. Boichuk, “Linear Noetherian boundary-value problems for differential systems with pulse influence,“Ukr. Mat. Zh.,44, No 3, 582–586 (1992).

    Google Scholar 

  4. A. A. Boichuk, N. A. Perestyuk, and A. M. Samoilenko, “Periodic solutions of momentum differential systems for critical cases,“Diff. Uravn., No 9, 1516–1521 (1991).

    Google Scholar 

  5. I. G. Malkin,Some Problems in the Theory of Nonlinear Oscillations [in Russian], Gostekhisdat, Moscow (1956).

    Google Scholar 

  6. E. A. Grebennikov and Yu. A. Ryabov,Constructive Methods in the Analysis of Nonlinear Systems [in Russian], Nauka, Moscow (1979).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Geophysics, Ukrainian Academy of Sciences, Ukraine

    A. A. Boichuk

  2. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev

    R. F. Khrashchevskaya

Authors
  1. A. A. Boichuk
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. F. Khrashchevskaya
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 2, pp. 221–225, February, 1993.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Boichuk, A.A., Khrashchevskaya, R.F. Weakly nonlinear boundary-value problems for differential systems with pulse influence. Ukr Math J 45, 235–240 (1993). https://doi.org/10.1007/BF01060978

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01060978

Keywords

Search

Navigation