  In this paper, starting from the Bogoliubov-Born-Green-Yvon equations of the
liquid-state theory, we formulate two equivalent approaches for the calculation
of the total density profile and of the charge density profile of ionic fluids
near nonplanar charged surfaces. In the framework of these approaches, we
establish exact conditions, that a particular point of these profiles should
satisfy, in the form of contact theorems. These contact theorems for the total
density profile and the charge density profile are obtained by direct
integration of a system of equations derived from the
Bogoliubov-Born-Green-Yvon equations. The contact theorems for both profiles
have nonlocal character. It is shown that the contact value of the total
density profile for uncharged surfaces is characterized by the bulk pressure
and the surface tension. The contact theorems are applied to the cases of
spherical and cylindrical surfaces. It is shown that the contact theorem for
the total density profile coincides with the recent results obtained by W.
Silvester-Alcantara, D. Henderson and L.B. Bhuiyan Mol. Phys., 113, 3403, 2015

Soft Condensed Matter