  The stability conditions for the singular vortex which accompanies Majorana
zero modes at the core are investigated for p-wave resonant superfluids of
atomic Fermi gases. Within the Ginzburg-Landau framework we determine the
stable conditions in the parameter space for the external rotation frequency
and the harmonic trap frequency. There exists the narrow stable region in this
parameter space for quasi-two-dimensional condensates. We also describe the
detailed characterizations of the spatial structure of the order parameter in
the chiral p-wave superfluids under rotation.
