Freidlin–Wentzell's large deviations for stochastic evolution equations

We prove a Freidlin–Wentzell large deviation principle for general stochastic evolution equations with small perturbation multiplicative noises. In particular, our general result can be used to deal with a large class of quasi-linear stochastic partial differential equations, such as stochastic porous medium equations and stochastic reaction–diffusion equations with polynomial growth zero order term and p-Laplacian second order term.