The steady-state Vlasov equations for a monotonic electric potential

A large class of solutions to the steady-state Vlasov equations for a two component one-dimensional plasma for which the electric potential ø is monotonic is shown to exist. Some of these solutions are shock-like in the sense that the particle densities are also monotonic. If the particle and energy densities at infinity are not constraints of the problem, it is shown that there are always solutions for an arbitrary monotonic ø, and the solutions themselves contain arbitrary functions.