  We study supergravity BPS equations which correspond to mass-deformation of
some representative AdS/CFT examples. The field theory of interest are N=4, D=4
super Yang-Mills, the ABJM model in D=3, and the Brandhuber-Oz fixed point in
D=5. For these gauge theories the free energy with mass terms for matter
multiplets is calculable in large-N limit using supersymmetric localization
technique. We suggest a perturbative method to solve the supergravity
equations. For the dual of mass-deformed ABJM model we reproduce the known
exact solutions. For the mass-deformed Brandhuber-Oz theory our method gives
the holographic free energy in analytic form. For N=2* theory our result is in
good agreement with the localization result.

High Energy Physics - Theory