Existence and asymptotic behavior of square-mean S-asymptotically periodic solutions for stochastic evolution equation involving delay

Abstract

. This paper studies the stochastic evolution equations with fi nite delay. By means of the compact semigroup theory and Schauder fi xed point theorem, the existence of square-mean S -asymptotically periodic mild solutions is obtained under certain growth conditions. In addition, using the contraction mapping principle and Gronwall integral inequality, the uniqueness and global asymptotic stability of the square-mean S -asymptotically periodic mild solutions are discussed. Finally, an example is given to illustrate our abstract results.