  The Freidlin-Wentzell large deviation principle is established for the
distributions of stochastic evolution equations with general monotone drift and
small multiplicative noise. As examples, the main results are applied to derive
the large deviation principle for different types of SPDE such as stochastic
reaction-diffusion equations, stochastic porous media equations and fast
diffusion equations, and the stochastic p-Laplace equation in Hilbert space.
The weak convergence approach is employed in the proof to establish the Laplace
principle, which is equivalent to the large deviation principle in our
framework.
