Nontrivial solvability of the homogeneous Wiener-Hopf multiple integral equation in the conservative case and the Peierls equation (Q2193758)

The paper concerns an integral operator of convolution type in an octant. The kernel is positive with Lebesgue integrable singularities. Extending the preceding results for the two-dimensional case in [\textit{L. G. Arabadzhyan}, Math. Notes 106, No. 1, 3--10 (2019; Zbl 1439.45003); translation from Mat. Zametki 106, No. 1, 3--12 (2019)], the authors prove here, under additional assumptions, the existence of a positive solution for the corresponding equation of second type. A precise bound for the algebraic growth of the solution at infinity is also given. As a particular case, results are deduced for the so-called Peierls equation, appearing in the theory of radiation transfer, see [\textit{E. Hopf}, Mathematical problems of radiative equilibrium. Cambridge: Cambridge University Press (1934; JFM 60.0809.01)].