A simple field theoretical model is considered for an electrified interface in which the electrolyte solution is in contact with a charged hard wall. The model for the electrolyte includes Coulombic interactions, local ideal entropy, functional and specific nonlocal interactions. For the specific nonlocal interactions, the simplest form of the square gradient term is selected. The charged hard wall is characterized by an additional short range potential reduced to the form of a Dirac function. An exact relation, analogous to Maxwell relations in thermodynamics, is derived describing the effect of the wall specificity on the electric properties. In the mean held theory, the consistency equations for the ionic profiles are solved analytically in the Limit of small charge densities and weak wall potentials. The electric double layer structure is discussed in terms of two characteristic lengths-Debye length for electrostatics and the characteristic length for the specific interaction. We also present and discuss charge and density profiles of ions calculated numerically by it differential equation solver. With the results thus obtained we find a behavior much different from the classical Gouy-Chapman theory.