Stationary solutions of boundary value problems for a Maxwell-Boltzmann system modelling degenerate semiconductors

One of the most accurate models for carrier transport in semiconductors is based on the Maxwell-Boltzmann system. Degeneracy effects are taken into account by the nonlinearity of the collisions operator. We use two recent techniques developed for the study of kinetic models, upper solutions and mean compactness results, to prove existence of stationary solutions with arbitrary large boundary data, in any kind of geometries.