Abstract

The paper is devoted to the study of a class of integral equations with a symmetric kernel and with convex nonlinearity on the positive semiaxis. Existence and uniqueness theorems for a nonnegative and bounded solution are proved. The qualitative properties of the constructed solution are investigated. At the end of the paper, some particular examples for the above mentioned class of equations, having direct applications in the \(p\)-adic open-closed string dynamic theory and in the theory of geographical spread of epidemics, are given.

中文翻译：

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关于半轴上具有凸非线性的一类积分方程

摘要

本文致力于一类具有对称核且在正半轴上具有凸非线性的积分方程的研究。证明了一个非负有界解的存在性和唯一性定理。研究了所构造溶液的定性性质。在本文的最后，给出了上述方程组的一些特定示例，这些示例直接应用于\（p \）- adic开闭弦动力学理论和流行病的地理传播理论。