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Ukrainian Mathematical Journal

, Volume 50, Issue 2, pp 186–195 | Cite as

Nonlinear boundary-value problems for systems of ordinary differential equations

  • A. A. Boichuk
Article

Abstract

We consider nonlinear boundary-value problems (with Noetherian operator in the linear part) for systems of ordinary differential equations in the neighborhood of generating solutions. By using the Lyapunov — Schmidt method, we establish conditions for the existence of solutions of these boundary-value problems and propose iteration algorithms for their construction.

Keywords

Ordinary Differential Equation Null Space Matrix Pseudoinverse Noetherian Operator Generalize Inverse Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    A. A. Boichuk, V. F. Zhuravlev, and A. M. Samoilenko, Generalized Inverse Operators and Noetherian Boundary-Value Problems [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1995).Google Scholar
  2. 2.
    I. G. Malkin, Some Problems of the Theory of Nonlinear Oscillations [in Russian], Gostekhizdat, Moscow (1956).MATHGoogle Scholar
  3. 3.
    E. A. Grebenikov and Yu. A. Ryabov, Constructive Methods for the Analysis of Nonlinear Systems [in Russian], Nauka, Moscow (1979).Google Scholar
  4. 4.
    A. M. Samoilenko and N. I. Ronto, Numerical-Analytic Methods for the Investigation of Solutions of Boundary-Value Problems [in Russian], Naukova Dumka, Kiev (1986).Google Scholar

Copyright information

© Plenum Publishing Corporation 1998

Authors and Affiliations

  • A. A. Boichuk
    • 1
  1. 1.Institute of MathematicsUkrainian Academy of SciencesKiev

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