We consider a nonlinear integral equation on the whole line with a Hammerstein-Stieltjes integral operator whose pre-kernel is a continuous distribution function. Under certain conditions imposed on the nonlinearity, we prove constructive existence and uniqueness theorems for nonnegative monotone bounded solutions. Some qualitative properties of the constructed solution are also studied. In particular, the results proved in the paper contain a theorem of O. Diekmann as a special case.

中文翻译：

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整行上一类非线性Hammerstein-Stieltjes积分方程的可解性

我们使用Hammerstein-Stieltjes积分算子在整行上考虑一个非线性积分方程，该算子的前核是连续分布函数。在一定的非线性条件下，我们证明了非负单调有界解的构造性存在性和唯一性定理。还研究了所构造溶液的一些定性性质。特别是，本文证明的结果包含O. Diekmann定理作为特例。