Abstract and Applied Analysis
- Abstr. Appl. Anal.
- Volume 2014, Special Issue (2014), Article ID 934534, 11 pages.
Asymptotically Almost Periodic Solutions for a Class of Stochastic Functional Differential Equations
This work is concerned with the quadratic-mean asymptotically almost periodic mild solutions for a class of stochastic functional differential equations . A new criterion ensuring the existence and uniqueness of the quadratic-mean asymptotically almost periodic mild solutions for the system is presented. The condition of being uniformly exponentially stable of the strongly continuous semigroup is essentially removed, which is generated by the linear densely defined operator , only using the exponential trichotomy of the system, which reflects a deeper analysis of the behavior of solutions of the system. In this case the asymptotic behavior is described through the splitting of the main space into stable, unstable, and central subspaces at each point from the flow’s domain. An example is also given to illustrate our results.
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 934534, 11 pages.
First available in Project Euclid: 27 February 2015
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Liu, Aimin; Liu, Yongjian; Liu, Qun. Asymptotically Almost Periodic Solutions for a Class of Stochastic Functional Differential Equations. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 934534, 11 pages. doi:10.1155/2014/934534. https://projecteuclid.org/euclid.aaa/1425048246