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


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.


Ordinary Differential Equation Null Space Matrix Pseudoinverse Noetherian Operator Generalize Inverse Operator 
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  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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