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<p>We consider weakly nonlinear Fredholm integrodifferential equations with degenerate kernel in Banach spaces. Necessary conditions are established for the existence of a solution, which turns into the generating solution for ε = 0<i>.</i> We also obtain sufficient conditions for the existence of at least one solution and construct a convergent iterative algorithm for its determination.</p>

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Weakly Nonlinear Fredholm Integrodifferential Equations with Degenerate Kernel in Banach Spaces

  • 期刊论文

  • 发表日期：

    2025年3月1日

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  • Valerii Zhuravliov,
  • Mykola Fomin

摘要

We consider weakly nonlinear Fredholm integrodifferential equations with degenerate kernel in Banach spaces. Necessary conditions are established for the existence of a solution, which turns into the generating solution for ε = 0. We also obtain sufficient conditions for the existence of at least one solution and construct a convergent iterative algorithm for its determination.