We study one class of nonlinear Urysohn integral equations in a quadrant of the plane. It is assumed that, for the corresponding two-dimensional Urysohn operator, some Hammerstein operator with power nonlinearity serves as a minorant in the sense of M. A. Krasnosel’skiĭ.We prove the existence of a nonnegative (nontrivial) and bounded solution for such equations.

中文翻译：

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一类二维Urysohn积分方程的可解性

我们研究平面象限中的一类非线性Urysohn积分方程。假设对于相应的二维Urysohn算子，具有一定功率非线性的Hammerstein算子在MAKrasnosel'skiĭ的意义上是次要的，我们证明了此类方程存在非负（非平凡）有界解。