Existence of Optimal Mild Solutions for Multi-valued Impulsive Stochastic Partial Functional Integrodifferential Equations

Abstract

In this paper, we introduce a new class of multi-valued impulsive stochastic partial functional integrodifferential equations with infinite delay in the $$\alpha $$ -norm. Using stochastic analysis, analytic semigroup and fixed point strategy with the properties of fractional powers of closed operators, we establish the existence and uniqueness results of mild solutions for these equations with not instantaneous impulse. Then, the existence of optimal mild solutions is also proved. Particularly, the compactness of the operator semigroups is not needed. Finally, an example to illustrate the applications of main results is given.