Abstract: It has been shown that stable equilibrium density profiles found within the gradient approximation of the molecular density functional theory in concentric vapor shells surrounding nonwettable nanoparticles immersed in a liquid phase are also observed within the framework of the integral density functional theory and nudged elastic band method. In all used approaches, the stable profiles correspond to the minimum in the grand thermodynamic potential of the entire system consisting of a particle, a vapor interlayer, and bulk liquid. The results obtained by all three methods have been compared at the same parameters of the potential of intermolecular interaction and the interaction with particle molecules. The comparison has shown that the gradient approximation somewhat overestimates the thickness of the vapor interlayer, while being in qualitative agreement with other approaches. The boundary condition for the molecular density of a fluid on a substrate has been discussed.