On solution of a class of Hammerstein type nonlinear integral equations on the positive half-line in the critical case

In the this article a class of nonlinear integral equations with noncompact Hammerstein integral operator, the kernel of which depends on difference of its arguments is investigated. Above mentioned class of equations arises in the kinetic theory of gases and in the radiative transfer theory in nuclear reaction.
Combination of special iteration methods with the methods of the theory of construction of invariant cone-shaped segments allow to prove existence theorems of positive solutions in special selected weighted space.