On the solvability of one class of two-dimensional Urysohn integral equations

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.