  In a previous paper (arXiv:1309.2204, JHEP 1311 (2013) 087), we present a
holographic s+p superconductor model with a scalar triplet charged under an
SU(2) gauge field in the bulk. We also study the competition and coexistence of
the s-wave and p-wave orders in the probe limit. In this work we continue to
study the model by considering the full back-reaction The model shows a rich
phase structure and various condensate behaviors such as the "n-type" and
"u-type" ones, which are also known as reentrant phase transitions in condensed
matter physics. The phase transitions to the p-wave phase or s+p coexisting
phase become first order in strong back-reaction cases. In these first order
phase transitions, the free energy curve always forms a swallow tail shape, in
which the unstable s+p solution can also play an important role. The phase
diagrams of this model are given in terms of the dimension of the scalar order
and the temperature in the cases of eight different values of the back reaction
parameter, which show that the region for the s+p coexisting phase is enlarged
with a small or medium back reaction parameter, but is reduced in the strong
back-reaction cases.
