Existence and stability results of mild solutions for random impulsive stochastic partial differential equations with noncompact semigroups

In this paper, we study the existence and some stability results of mild solutions for random impulsive stochastic partial differential equations with noncompact semigroups in Hilbert spaces. Initially, we prove the existence of mild solutions by using Hausdorff measures of noncompactness and the Mönch fixed point theorem. Then, we explore the stability with continuous dependence of initial conditions, Hyers–Ulam stability and mean-square stability of the system by developing some new analysis techniques and establishing an improved inequality. Finally, an example is given to illustrate the abstract results obtained in this paper.