  In this paper we propose an all-in-one statement which includes existence,
uniqueness, regularity, and numerical approximations of mild solutions for a
class of stochastic partial differential equations (SPDEs) with non-globally
monotone nonlinearities. The proof of this result exploits the properties of an
existent fully explicit space-time discrete approximation scheme and, in
particular, the fact that it satisfies suitable a priori estimates. As a
byproduct we obtain almost sure and strong convergence of the approximation
scheme to the mild solutions of the considered SPDEs. We conclude by applying
the main result of the paper to the stochastic Burgers equations with
space-time white noise.
