Square-mean piecewise almost automorphic mild solutions to a class of impulsive stochastic evolution equations

Abstract

Abstract In this paper, we introduce the concept of square-mean piecewise almost automorphic function. By using the theory of semigroups of operators and the contraction mapping principle, the existence of square-mean piecewise almost automorphic mild solutions for linear and nonlinear impulsive stochastic evolution equations is investigated. In addition, the exponential stability of square-mean piecewise almost automorphic mild solutions for nonlinear impulsive stochastic evolution equations is obtained by the generalized Gronwall–Bellman inequality. Finally, we provide an illustrative example to justify the results.

Keywords

• Square-mean piecewise almost automorphic function
• Theory of semigroups of operators
• Contraction mapping principle
• Impulsive stochastic evolution equations
• Generalized Gronwall–Bellman inequality