Now that we have written down the guessed grand potential functionals and we have coupled them to the corresponding Poisson-Boltzmann differential equations, we can minimize the grand potentials with respect to the density functions and obtain corresponding Euler-Lagrange equations. By inserting the calculated density functions into Poisson-Boltzmann equations, and applying the boundary conditions, we can obtain the following results for density profiles and electrostatic potential in the region inside the brush,