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<p>We investigate a weakly nonlinear boundary-value problem for a system of differential equations with delay. The initial function of the differential system with delay contains an unknown eigenfunction guaranteeing the solvability of the weakly nonlinear boundary-value problem. By using the Adomian decomposition method, we establish the conditions of solvability and develop a new iterative technique aimed at solving a weakly nonlinear boundary-value problem for a system of differential equations with delay as well as at finding its eigenfunction.</p>

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ADOMIAN DECOMPOSITION METHOD IN THE THEORY OF PROBLEMS INVERSE TO NONLINEAR BOUNDARY-VALUE PROBLEMS WITH DELAY

  • 期刊论文

  • 发表日期：

    2025年7月31日

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  • Oleksandr Boichuk,
  • Sergiy Chuiko,
  • Viktor Chuiko

摘要

We investigate a weakly nonlinear boundary-value problem for a system of differential equations with delay. The initial function of the differential system with delay contains an unknown eigenfunction guaranteeing the solvability of the weakly nonlinear boundary-value problem. By using the Adomian decomposition method, we establish the conditions of solvability and develop a new iterative technique aimed at solving a weakly nonlinear boundary-value problem for a system of differential equations with delay as well as at finding its eigenfunction.