Journal of Mathematical Sciences

, Volume 223, Issue 3, pp 337–350 | Cite as

Weakly Nonlinear Matrix Boundary-Value Problem in the Case of Parametric Resonance

  • S. M. Chuiko
  • A. S. Chuiko
  • D. V. Sysoev

We establish necessary and sufficient conditions for the existence of solutions of a nonlinear matrix boundary-value problem for a system of ordinary differential equations in the case of parametric resonance. We construct a convergent iterative scheme for finding approximate solutions of the problem. As an example of application of the proposed iterative scheme, we obtain approximations to the solutions of a periodic boundary-value problem for the Riccati-type equation with parametric perturbation. To check the accuracy of the obtained approximations, we introduce residuals in the original equation.


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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  • S. M. Chuiko
    • 1
  • A. S. Chuiko
    • 1
  • D. V. Sysoev
    • 1
  1. 1.Donbass State Pedagogic UniversitySlavyanskUkraine

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