We show the existence of solutions to the charge conserved Poisson–Boltzmann equation with a Dirichlet boundary condition on . Here is a smooth simply connected bounded domain in with . When , the solutions can have isolated singularities at prescribed points in , in which case they are essentially weak solutions of the charge conserved Poisson–Boltzmann equations with Dirac measures as source terms. By contrast, for higher dimensional cases , all the isolated singularities are removable. As a small parameter tends to zero, and the solutions develop a Debye boundary layer near the boundary . In the interior of , the solutions converge to a unique constant. The limiting constant is explicitly calculated in terms of a novel formula which depends only on the supplied Dirichlet data on . In addition we also give a quantitative description on the asymptotic behaviour of the solutions as .