Asymptotically almost periodic solutions of stochastic functional differential equations

2011 ◽  
Vol 218 (5) ◽  
pp. 1499-1511 ◽  
Author(s):  
Junfei Cao ◽  
Qigui Yang ◽  
Zaitang Huang ◽  
Qing Liu
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Functional Differential Equations ◽  
Almost Periodic Solutions ◽  
Stochastic Functional Differential Equations ◽  
Almost Periodic ◽  
Functional Differential ◽  
Asymptotically Almost Periodic ◽  
Stochastic Functional

scholarly journals Almost Periodic Solutions to Impulsive Stochastic Delay Differential Equations Driven by Fractional Brownian Motion With 12 < H < 1

2021 ◽  
Vol 9 ◽  
Author(s):  
Lili Gao ◽  
Xichao Sun
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Fractional Brownian Motion ◽  
Functional Differential Equations ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Stochastic Delay Differential Equations ◽  
Functional Differential ◽  
Stochastic Functional

In this article, we study the existence and uniqueness of square-mean piecewise almost periodic solutions to a class of impulsive stochastic functional differential equations driven by fractional Brownian motion. Moreover, the stability of the mild solution is obtained. To illustrate the results obtained in the paper, an impulsive stochastic functional differential equation driven by fractional Brownian motion is considered.

scholarly journals Asymptotically Almost Periodic Solutions for a Class of Stochastic Functional Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Aimin Liu ◽  
Yongjian Liu ◽  
Qun Liu
Keyword(s):  
Differential Equations ◽  
Mild Solutions ◽  
Functional Differential Equations ◽  
Stochastic Functional Differential Equations ◽  
Almost Periodic ◽  
Quadratic Mean ◽  
Exponential Trichotomy ◽  
Functional Differential ◽  
Asymptotically Almost Periodic ◽  
Stochastic Functional

This work is concerned with the quadratic-mean asymptotically almost periodic mild solutions for a class of stochastic functional differential equationsdxt=Atxt+Ft,xt,xtdt+H(t,xt,xt)∘dW(t). 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{Tt}t≥0is essentially removed, which is generated by the linear densely defined operatorA∶D(A)⊂L2(ℙ,ℍ)→L2(ℙ,ℍ), 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.

scholarly journals Existence of Almost Periodic Solutions for Impulsive Neutral Functional Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Junwei Liu ◽  
Chuanyi Zhang
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Functional Differential Equations ◽  
Continuous Operator ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Neutral Functional Differential Equations ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Exponentially Stable ◽  
Functional Differential

The existence of piecewise almost periodic solutions for impulsive neutral functional differential equations in Banach space is investigated. Our results are based on Krasnoselskii’s fixed-point theorem combined with an exponentially stable strongly continuous operator semigroup. An example is given to illustrate the theory.

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