Impulsive-integral inequality and exponential stability for stochastic partial differential equations with delays

In this letter, by establishing an impulsive-integral inequality, some sufficient conditions about the exponential stability in -moment of mild solution for impulsive stochastic partial differential equation with delays are obtained. The results in Caraballo and Liu [Caraballo, T. and Liu, K., 1999a. Exponential stability of mild solutions of stochastic partial differential equations with delays. Stoch. Anal. Appl. 17, 743-763] and Luo [Luo, J., 2008b. Fixed points and exponential stability of mild solutions of stochastic partial differential equation with delays. J. Math. Anal. Appl. 342, 753-760] are generalized and improved.