On positive solutions of one class of nonlinear integral equations of Hammerstein–Nemytskiĭ type on the whole axis

This paper is devoted to studying one class of nonlinear integral equations of Hammerstein–Nemytskiĭ type on the whole axis, which occurs in the theory of transfer in inhomogeneous medium. It is proved that these equations can be solved in various function spaces, and the asymptotic behaviour at infinity of the solutions that are constructed is studied.