  We investigate the holographic p-wave superfluid in the background metric of
the AdS soliton with $RF^{2}$ corrections. Two models, namely, the Maxwell
complex vector field model and Yang-Mills theory, are studied in the above
context by employing the Sturm-Liouville approach as well as the shooting
method. When turning on the spatial components of the gauge field, one observes
that, in the probe limit, the inclusion of $RF^{2}$ corrections hinders the
superfluid phase transition. On the other hand, however, in the absence of the
superfluid velocity, it is found that the $RF^2$ corrections lead to distinct
effects for the two models. Regardless of either the $RF^2$ correction or the
spatial component of the gauge field, the phase transition of the system is
observed to be always of the second order. Moreover, a linear relationship
between the charge density and chemical potential is largely established near
the critical point in both holographic superfluid models.
