希尔伯特空间中非局部随机积分微分系统的近似可控性
Approximate Controllability of Nonlocal Stochastic Integrodifferential System in Hilbert Spaces
AI总结：
本文在希尔伯特空间中研究非局部随机积分微分系统的近似可控性，利用Schauder定理和Grimmer理论，结合近似方法和对角线论证，验证了系统的可控性。
摘要：
本项目研究了在希尔伯特空间中具有非局部初始条件的一类随机积分微分方程的近似可控性。与文献中常见的关注点不同，我们不考虑非局部项的紧性和利普希茨条件。我们利用解析算子是紧算子的事实。首先，我们利用Schauder固定点定理证明非线性系统的可控性，这是一种以鲁棒性著称的方法；同时，我们还使用Grimmer的解析算子理论。随后，我们利用可靠的近似方法和强大的对角线论证法来确定随机系统的近似可控性。最后，我们提供一个例子来验证我们的理论陈述。
英文摘要：
This project investigates the approximate controllability of a class of stochastic integrodifferential equations in Hilbert space with non-local beginning conditions. In a departure from the conventional concerns expressed in the literature, we will not consider compactness or the Lipschitz criteria concerning the nonlocal term. We use the fact that the resolvent operator is compact. We first prove the controllability of the nonlinear system using Schauder's fixed point theorem, a method known for its robustness; as well, we also use Grimmer's resolvent operator theory. Subsequently, we employ the reliable approximation methods and the powerful diagonal argument to determine the approximate controllability of the stochastic system. To conclude, we present an example that validates our theoretical statement.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
