  We establish well-posedness in the mild sense for a class of stochastic
semilinear evolution equations with a polynomially growing quasi-monotone
nonlinearity and multiplicative Poisson noise. We also study existence and
uniqueness of invariant measures for the associated semigroup in the Markovian
case. A key role is played by a new maximal inequality for stochastic
convolutions in $L_p$ spaces.
