Sufficient conditions for the solvability of the Urysohn integral equation on a half-line

A study was conducted to demonstrate sufficient conditions for the solvability of the Urysohn integral equation on a half-line. The Urysohn integral equation on a half line with the unknown function had a nonnegative continuous function with the property that there exist a number η > 0. This integral equation can be used for various applications in mathematical physics, radiative transfer theory, the kinetic theory of gases, continuum mechanics, and econometrics. It was observed that the limit of the solution was found at infinity and a lower bound for the solution was given using VA Ambartsumyan's function. It was also found that Ambartsumyan functions satisfied the system of nonlinear functional equations.