Abstract

This paper is devoted to the study of existence and uniqueness of the solution of a class of nonlinear two-dimensional integral equations in the plane. Such equations arise in theory of \(p\)-adic strings. In addition, equations of this nature are encountered in mathematical epidemiology. Constructive existence and uniqueness theorems for a positive bounded solution are proved. We also obtain the integral asymptotic of the solution. At the end of the paper applied examples of this equation are given.

中文翻译：

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关于 $$p$$ -Adic 串理论中二维非线性积分方程的构造可解性

摘要

本文致力于研究一类平面内非线性二维积分方程解的存在唯一性。这样的方程出现在\(p\) -adic 字符串的理论中。此外，在数学流行病学中会遇到这种性质的方程。证明了正有界解的构造存在性和唯一性定理。我们还获得了解的积分渐近。文末给出了该方程的应用实例。