  In this article we consider existence and uniqueness of the solutions to a
large class of stochastic partial differential of form $\partial_t u = L_x u +
b(t,u)+\sigma(t,u)\dot{W}$, driven by a Gaussian noise $\dot{W}$, white in time
and spatial correlations given by a generic covariance $\gamma$. We provide
natural conditions under which classical Picard iteration procedure provides a
unique solution. We illustrate the applicability of our general result by
providing several interesting particular choices for the operator $L_x$ under
which our existence and uniqueness result hold. In particular, we show that
Dalang condition given in Dalang (1999) is sufficient in the case of many
parabolic and hypoelliptic operators $L_x$.
