  We study the interplay of spin-orbit coupling (SOC) and strong p-wave
interaction to the scattering property of spin-1/2 ultracold Fermi gases. Based
on a two-channel square-well potential generating p-wave resonance, we show
that the presence of an isotropic SOC, even for its length much longer than the
potential range, can greatly modify the p-wave short-range boundary
condition(BC). As a result, the conventional p-wave BC cannot predict the
induced molecules near p-wave resonance, which can be fully destroyed to vanish
due to strong interference between s- and p-wave channels. By analyzing the
intrinsic reasons for the breakdown of conventional BC, we propose a new p-wave
BC that can excellently reproduce the exact molecule solutions and also equally
apply for a wide class of single-particle potentials besides SOC. This work
reveals the significant effect of SOC to both the short- and long-range
properties of fermions near p-wave resonance, paving the way for future
exploring interesting few- and many-body physics in such system.
