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<p>We establish constructive necessary and sufficient conditions of solvability and propose a scheme for the construction of solutions of a nonlinear autonomous boundary-value problem unsolved with respect to the derivative. We also construct convergent iterative schemes for finding approximations to the solutions of a nonlinear autonomous boundary-value problem unsolved with respect to the derivative. As examples of application of the obtained iterative schemes, we find approximations to the solutions of periodic boundary-value problems for Liénard-type equations unsolved with respect to the derivative.</p>

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Autonomous Boundary-Value Problem Unsolved with Respect to the Derivative

  • 期刊论文

  • 发表日期：

    2025年1月1日

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  • Sergiy Chuiko,
  • Olena Chuiko,
  • Daria Diachenko

摘要

We establish constructive necessary and sufficient conditions of solvability and propose a scheme for the construction of solutions of a nonlinear autonomous boundary-value problem unsolved with respect to the derivative. We also construct convergent iterative schemes for finding approximations to the solutions of a nonlinear autonomous boundary-value problem unsolved with respect to the derivative. As examples of application of the obtained iterative schemes, we find approximations to the solutions of periodic boundary-value problems for Liénard-type equations unsolved with respect to the derivative.