Abstract:
In the study of integrodifferential evolution equations, systems may be disturbed by white noise or other stochastic factors, which affect the operational results of the model. Meanwhile, when subjected to external influences at certain moments, the system will undergo instantaneous state changes. Although such changes are extremely short-lived compared to the entire time evolution process, they may affect the overall performance and final results of the model, this phenomenon is known as the impulse phenomenon. Therefore, it is necessary to establish a stochastic integrodifferential equation model with instantaneous impulses. In this paper, we investigate the exact controllability of a class of second-order neutral stochastic integrodifferential equations with nonlocal conditions and instantaneous impulses in Hilbert spaces. Since the equation does not contain a control term, the constraint conditions satisfied by the control operator are given separately. Thus, we first use the technique of variable substitution and the relevant theory of strongly continuous cosine operator families to redefine new operators, get the express of the mild solution of the studied problem and also establishes a theoretical foundation for the subsequent exact controllability. Subsequently, the existence result of mild solutions and sufficient conditions for the exact controllability of the studied problem are derived by employing mathematical tools such as the theory of stochastic analysis, H \ddot\mathrmo lder inequality and Sadovskii fixed point theorem. The results obtained further enrich the theoretical research on integrodifferential evolution equations.