  We present an approach for determining susceptibilities and order parameters
in multi-band Hubbard model within functional renormalization group method, and
apply it to study various instabilities of the FeAs-based high temperature
superconductor. First, we derive the formulae of susceptibilities and order
parameters of superconducting parings, spin density waves and charge density
waves with diverse wave vectors which could occur in multi-band Hubbard model.
Second, we apply it to the FeAs-based high temperature superconductor and find
an electronic-driven superconducting pairing instability within a five band
model with pure repulsive interactions. Our study shows that for doping of our
concern, there is competition between antiferromagnetic and superconducting
instabilities. In addition, we show that for doping of 0.1, the susceptibility
of extended s-wave pairing is dominant over others, while a staggered
superconducting pairing with has the second largest value of susceptibility.
