Nontrivial solvability of the homogeneous Wiener–Hopf multiple integral equation in the conservative case and the Peierls equation

We describe the process of constructing a positive solution of the homogeneous Wiener–Hopf integral equation in an octant in a special (conservative) case. Applying the obtained general results to the homogeneous stationary Peierls equation allows studying the behavior of the solutions of this equation for large argument values. These problems are particularly interesting in the theory of radiation transfer.