  We study effects of quantum fluctuations on two-dimensional $p+ip$
superfluids near resonance. In the standard paradigm, phase transitions between
superfluids and zero density vacuum are continuous. When strong quantum
fluctuations near resonance are taken into account, the line of continuous
phase transitions terminates at two multicritical points near resonance,
between which the transitions are expected to be first-order ones. The size of
the window where first-order phase transitions occur is shown to be substantial
when the coupling is strong. Near first-order transitions, superfluids
self-contract due to phase separations between superfluids and vacuum.
