We present Vlasov equilibria characterized by discontinuous distribution functions of electrons and of finite mass ions and by asymmetric electric potential profiles. These profiles well reproduce double layers, phase space holes,
solitary waves, sheaths near electrodes and near surfaces of airless bodies in Space. By means of the energy method, we show that the stability of the proposed equilibria is better than that of the steady-state solutions of the Vlasov equation based on continuous distribution functions and symmetric potential profiles
