we obtain For T → T$_{c}$ we have 1 /ξ$_{b}$ → 0 where 1 /ξ$_{b}$ = λ$_{1}$ or 1 /ξ$_{b}$ = λ$_{2}$ for J > 0 or J < 0 respectively (see sec.II C), and the equations (57) take the form From the boundary conditions and Eq.(59) we obtain in this case Note that the linearized equations for φ and ( η, ϑ ) are decoupled. Thus, at the linear order there is no effect of the concentration profile on the charge distribution. Similar result was obtained recently in Ref.[19]. Note, however that we consider a simplified model of SR interactions, Eq.(8), where direct SR couplings between the charge and the concentration are disregarded. Beyond the linear order the coupling between the EL equations leads to modifications of the charge and concentration profiles. Note that the solution of the nonlinear equations can be written in the form (50) when all amplitudes of the solutions of the linearized equations are small and of the same order, κσ = O ( ν ), n$_{i}$ = O ( ν ) and t$_{i}$ = O ( ν ). This means a large Debye screening length and a small surface-charge density, as well as weak surface fields H$_{η}$, H$_{θ}$ (see Eqs. (62) (63)). We shall limit ourselves to such conditions and calculate the first correction ϑ $^{(2)}$, η $^{(2)}$, φ (2) to the solutions of the linearized equations. For the electrostatic part we obtain 17 ψ (2) = k$_{B}$T e ¯ ρ$_{c}$ [ φη ¯ ρ$_{c}$ − φ (2) ] (64) t$_{1}$ ≃$_{T}$$_{→}$$_{T}$ c − n$_{1}$ M$_{22}$ M$_{21}$ + ... (63) n$_{1}$ ≃$_{T}$$_{→}$$_{T}$ c − ( H$_{η}$M$_{11}$ − H$_{ϑ}$M$_{21}$ ) T r M + ... (62) η ( z ) ≃ n$_{1}$ exp( − z/ξ$_{b}$ ) . (61) ϑ ( z ) ≃ t$_{1}$ exp( − z/ξ$_{b}$ ) (60) t$_{i}$ n$_{i}$ = λ 2 i − M$_{22}$ M$_{21}$ . (59) B. Leading-order correction to the linearized EL equations