On solvability of a Hammerstein - Voltera type nonlinear system of integral equations in critical case

We consider Hammerstein-Voltera type nonlinear system of integral equations in critical case. Above mentioned equations have applications in rediative transfer theory and kinetic theory of gases. Using special iteration methods and method of monotone operators theory we prove the exitstence of by component positive solutions in space of bounded and summerable functions with zero limit at infinity. Some examples of corresponding equations representing separate interest are also given.