Double Layer Solutions of the Vlasov–Poisson System

Abstract

We consider the boundary value problem of the stationary Vlasov–Poisson system in a half line. In another paper, we clarified completely when there is a single layer solution, that is a solution whose electrostatic potential is monotone. In this paper, we study the possibility of the existence of double layer solutions whose electrostatic potential has a unique critical point and extremum.