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Abstract <p>We study the issues of existence of uniqueness and asymptotic behavior at infinity of the solution for one class of Urysohn integral equations with monotone nonlinearity. This class of equations, in addition to theoretical interest, has important applied significance in various areas of physics and biology.We prove a constructive theorem on the existence of a nonnegative continuous and bounded solution. We found the limit of the solution at infinity and establish that the difference between the limit and the solution is a summable function on the positive part of the real line.We also prove a theorem on the uniqueness of the solution in a certain subclass of functions bounded on half line. At the end, specific examples of the Urysohn kernel satisfying all the conditions of the proven theorems are demonstrated.</p>

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Constructive Solvability of a Class of Nonlinear Integral Equations of Urysohn Type

  • 期刊论文

  • 发表日期：

    2025年8月1日

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  • A. Kh. Khachatryan,
  • Kh. A. Khachatryan,
  • H. S. Petrosyan

摘要

Abstract

We study the issues of existence of uniqueness and asymptotic behavior at infinity of the solution for one class of Urysohn integral equations with monotone nonlinearity. This class of equations, in addition to theoretical interest, has important applied significance in various areas of physics and biology.We prove a constructive theorem on the existence of a nonnegative continuous and bounded solution. We found the limit of the solution at infinity and establish that the difference between the limit and the solution is a summable function on the positive part of the real line.We also prove a theorem on the uniqueness of the solution in a certain subclass of functions bounded on half line. At the end, specific examples of the Urysohn kernel satisfying all the conditions of the proven theorems are demonstrated.