  We investigate the phase transitions of holographic p-wave superconductors in
(4+1)-dimensional Einstein-Yang-Mills-Gauss-Bonnet theories, in a grand
canonical ensemble. Turning on the back-reaction of the Yang-Mills field, it is
found that the condensations of vector order parameter become harder if the
Gauss-Bonnet coefficient grows up or the back-reaction becomes stronger. In
particular, the vector order parameter exhibits the features of first order and
second order phase transitions, while only the second order phase transition is
observed in the probe limit. We discuss the roles that the Gauss-Bonnet term
and the back-reaction play in changing the order of phase transition.
