一类随机积分微分方程的伪概周期解

Pseudo Almost Periodic Solutions for a Kind of Stochastic Functional Integro-Differential Equations

在可分实Hilbert空间考虑一类随机积分微分方程在伪概周期环境下解的存在唯一性问题.基于不动点原理和随机分析技巧,给出了方程存在唯一伪概周期解的一组充分条件.研究表明,如果方程预解算子族指数稳定,即使时滞是无界单调不减函数,在适当的条件下,方程依然存在唯一伪概周期解.最后,给出实例加以验证.

This paper consider a kind of stochastic functional integro-differential equations in a real separable Hilbert space . Based on the fixed point principle and the stochastic analysis techniques, a set of sufficient conditions of the existence and uniqueness of pseudo almost periodic mild solutions is given for the equation with pseudo almost periodicty. Sup- posed that the resolvent operators of equation is exponentially stable. The obtaining results show that even if the delay is unbounded monotone nondecreasing, there exists a unique pseudo almost periodic solution for the pseudo almost periodic equation with the exponen- tially stable resolvent operator family. Finally, the paper provides an illustrative example to justify the practical usefulness of the established theoretical results.