We study a system of nonlinear singular integral equations with a sum-difference kernel on the positive half-line. Such a system occurs (in various representations) in many branches of mathematical physics and applied mathematics. In particular, one encounters a system of equations with a kernel representing a Gaussian distribution and with a power nonlinearity in the dynamic theory of p-adic open-closed strings; in the case when the nonlinearity has a certain exponential structure, such a system occurs in mathematical biology, namely, in the theory of the spatio-temporal distribution of an epidemic.

We prove constructive theorems on the existence of nonnegative nontrivial continuous and bounded solutions. We study the uniqueness and the asymptotic behavior of constructed solutions at infinity. In conclusion, we give concrete applied examples of the mentioned equations that satisfy all assumptions of the proved theorems.

我们研究了在正半线上具有求和差核的非线性奇异积分方程组。这样的系统出现在数学物理学和应用数学的许多分支中（以各种表示形式）。特别是，在p -adic开闭弦的动力学理论中，人们遇到了一个方程组，其中的一个核表示高斯分布，并且具有幂非线性。在非线性具有一定指数结构的情况下，这种系统发生在数学生物学中，即在流行的时空分布理论中。

我们证明了关于非负非平凡连续和有界解的存在性的构造性定理。我们研究了无穷大时构造解的唯一性和渐近行为。最后，我们给出满足所证明定理所有假设的上述方程的具体应用示例。