Abstract: Using the hyper-exponential recurrence criterion, a large deviation principle for the

occupation measure is derived for a class of non-linear monotone stochastic partial differential

equations, including stochastic p-Laplace equation, stochastic porous medium equation,

stochastic fast-diffusion equation driven by Brownian motions. Furthermore, we establish the

LDP results for the stochastic real Ginzburg-Landau equation driven by alpha-stable noises.

Based on joint works with Jie Xiong and Lihu Xu.