On the solvability of a class of nonlinear Urysohn integral equations on the positive half-line

The paper investigates the Urysohn's nonlinear integral equation on the positive half-line. Some special cases of this equation have specific applications in different areas of modern natural science. In particular, such equations arise in the kinetic theory of gases, in the theory of $p$-adic open-closed strings, in mathematical theory of the spatio-temporal spread of the epidemic, and in theory of radiative transfer in spectral lines. The existence theorem for nonnegative nontrivial and bounded solutions is proved. Some qualitative properties of the constructed solution are studied. Specific applied examples of the Urysohn's kernel satisfying all the conditions of the approved theorem are provided.