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<p>We study an overdetermined system of Volterra type integral equations with strongly special boundary lines consisting of a two-dimensional integral equation and two one-dimensional integral equations. Explicit solutions of the overdetermined system depending on the sign of coefficients can contain arbitrary constants. We obtain the consistency condition for equations of the system and study properties of the solutions. We state and solve Cauchy type problems with conditions on singular manifolds.</p>

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Explicit Solutions of an Overdetermined System of Volterra Type Integral Equations with Strongly Singular Lines

  • 期刊论文

  • 发表日期：

    2025年1月11日

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  • Lutfiya Rajabova,
  • Nusrat Rajabov,
  • Muhidin Khushvakhtzoda

摘要

We study an overdetermined system of Volterra type integral equations with strongly special boundary lines consisting of a two-dimensional integral equation and two one-dimensional integral equations. Explicit solutions of the overdetermined system depending on the sign of coefficients can contain arbitrary constants. We obtain the consistency condition for equations of the system and study properties of the solutions. We state and solve Cauchy type problems with conditions on singular manifolds.