AbstractA linear equation for a particle steady‐state transport process in a homogeneous slab of finite thickness with boundary conditions of general type is derived. This equation differs from the well‐known integral equation for no‐reentry boundary conditions because of the presence of a per‐turbance linear operator which describes the effect of the re‐emission of the particles incident at the wall. The properties of the resulting operator are investigated. The dependence of the first positive eigenvalue on physical parameters is studies in detail. The results obtained are enough to discuss the existence of a critical strictly positive solution of the physical problems which motivated this