Mild Solutions and Harnack Inequality for Functional SPDEs with Dini   Drift
  The existence and uniqueness of the mild solution for a class of functional SPDEs with multiplicative noise and a locally Dini continuous drift are proved. In addition, under a reasonable condition the solution is non-explosive. Moreover, Harnack inequalities are derived for the associated semigroup under certain global conditions, which is new even in the case without delay. 
Xing Huang and Shao-Qin Zhang
math.PR