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<p>We establish constructive conditions for the solvability and propose a scheme for finding the solutions of nonlinear boundary-value problems with concentrated delay in the case of parametric resonance by using the Adomian decomposition method. The initial function of the differential system with delay contains an unknown eigenfunction guaranteeing the solvability of a weakly nonlinear boundary-value problem. By using the Adomian decomposition method, we deduce the conditions of solvability and construct a new iterative scheme for finding the solutions of the weakly nonlinear boundary-value problem for a system of differential equations with delay, as well as its eigenfunction in the case of parametric resonance. We establish constructive conditions for the convergence of the proposed iterative scheme to the solution of the weakly nonlinear boundary-value problem, as well as its eigenfunction.</p>

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Adomian Decomposition Method in the Theory of Nonlinear Boundary-Value Problems with Delay Under the Conditions of Parametric Resonance

  • 期刊论文

  • 发表日期：

    2026年5月29日

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  • Oleksandr Boichuk,
  • Sergii Chuiko,
  • Viktor Chuiko

摘要

We establish constructive conditions for the solvability and propose a scheme for finding the solutions of nonlinear boundary-value problems with concentrated delay in the case of parametric resonance by using the Adomian decomposition method. The initial function of the differential system with delay contains an unknown eigenfunction guaranteeing the solvability of a weakly nonlinear boundary-value problem. By using the Adomian decomposition method, we deduce the conditions of solvability and construct a new iterative scheme for finding the solutions of the weakly nonlinear boundary-value problem for a system of differential equations with delay, as well as its eigenfunction in the case of parametric resonance. We establish constructive conditions for the convergence of the proposed iterative scheme to the solution of the weakly nonlinear boundary-value problem, as well as its eigenfunction.