On the construction of an integrable solution to one class of nonlinear integral equations of Hammerstein-Nemytskii type on the whole axis

We study one class of nonlinear integral equations of convolution type with the Hammerstein-Nemytskii operator on the whole axis. This class has direct applications in the kinetic theory of gases, the theory of p-adic open-closed strings, and the theory of radiative transfer. We prove a constructive theorem on the existence of a nontrivial nonnegative solution integrable on the whole axis. In the end of the paper, we give specific examples of such equations satisfying all conditions of the main theorem.