  Recently the calculation of holographic free energy for mass-deformed ABJM
model (mABJM) with ${\cal N}=2$ supersymmetry and $SU(3)\times U(1)$ global
symmetry was tackled by Bobev et al. in arXiv:1812.01026. We solve the
associated BPS equations, requiring IR regularity, using a perturbative method
proposed by one of us recently in axXiv:1902.00418. In particular, we provide
an analytic proof of a crucial conjecture made in arXiv:1812.01026 based on
numerical solutions: that the R-charge values of three chiral multiplets in
mABJM should be independent of the IR values of a hypermultiplet scalar, which
is holographically dual to the superpotential mass term.
