Abstract

A multidimensional convolution-type integral equations with concave nonlinearity is investigated. This equation arises in the mathematical theory of the geographic distribution of an epidemic. The combination of well-known multidimensional methods and operator methods for constructing invariant cone segments for such operators with methods of the theory of convolution-type integral operators and limit theorems of the function theory allow proving the existence of positive bounded solutions to such equations. The asymptotic behavior of the constructed solutions is also studied. In a specific cone segment, the uniqueness of the solution is also proved. Particular applied examples of these equations are given.

中文翻译：

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流行病地理分布数学理论中一类多维积分方程的可解性

摘要

研究了具有凹非线性的多维卷积型积分方程。这个方程出现在流行病地理分布的数学理论中。众所周知的多维方法和用于构造此类算子的不变锥段的算子方法与卷积型积分算子理论和函数论极限定理的方法的组合允许证明此类方程的正有界解的存在。还研究了构造解的渐近行为。在特定的锥段中，也证明了解的唯一性。给出了这些方程的具体应用示例。