Positivity and explosion in mean -norm of stochastic functional parabolic equations of retarded type

This work is concerned with a class of semilinear stochastic functional parabolic differential equations of retarded type. We first establish conditions to ensure the existence of a unique non-negative solution of the stochastic delay partial differential equation under investigation. Subsequently, the problem of explosive or blow-up solutions in mean L p -norm sense, p ≥ 1 , in a finite time to the stochastic system is considered. Several examples are given to illustrate the theory established in the work.