Abstract We consider the class of nonlinear multivariate Urysohn type integral equations in the critical case. For certain Urysohn kernels, this class of equations has applications in various problems of physics and biology. We prove a constructive theorem on existence of a positive bounded continuous solution. We also show that the corresponding iterations converge geometrically to this solution. The solution thus constructed is shown to be unique in a certain conical segment. We also give examples of Urysohn kernels satisfying the conditions of our theorems.
Petrosyan et al. (Sun,) studied this question.