二阶非线性中立型无限时滞随机微分包含的可控性

本文主要在希尔伯特空间中讨论了二阶非线性中立型无限时滞随机微分包含的可控性问题.利用凝聚不动点定理得到了系统可控的一个充分性条件.     

无限时滞中立型随机泛函微分方程解的存在唯一性

有限时滞随机泛函微分方程的存在唯一性已经得到较多的研究,但对于无限时滞随机泛函微分方程的性质极少.本文在不需要线性增长条件,在一致Lipschitz条件下证明了无限时滞中立型随机泛函微分方程的存在唯一性,给出了精确解和近似解的误差估计,最后给出了解的矩估计.     

Existence of Solutions of Nonlinear Neutral Stochastic Differential Inclusions in a Hilbert Space

Abstract

In this paper, the existence of mild solutions of a class of non-linear neutral stochastic differential inclusions in Hilbert space is studied. The results are obtained by using a new fixed point theorem for a condensing map due to Martelli. For an application of the result, the neutral stochastic reaction-diffusion inclusion is also discussed.     

Approximate Controllability of Neutral Stochastic Functional Differential Systems with Infinite Delay

In this article, we consider a class of control systems governed by the neutral stochastic functional differential equations with unbounded delay and study the approximate controllability of the system. An example is given to illustrate the result.     

中立型无限时滞带跳随机泛函微分方程解的存在唯一性

本文首先在Lipschiz条件和线性增长条件下,通过Picard迭代法研究了带跳的无限时滞中立型随机微分方程解的存在唯一性,接着对这这类方程的Picard迭代解与精确解的误差进行估计,最后讨论了解的矩估计。     

具有无限时滞的中立型高维周期微分系统的周期解

本文考虑中立型高维周期微分系统d/dt(x(t)+cx(t-r))=A(t,x(t-r(t)))x(t)+ ∫t-∞C(t,s)x(s)ds+f(t,xt)+b(t)的T-周期解的存在性问题,利用线性系统的指数型 二分性和Krasnoselskii不动点定理,建立了保证系统存在T-周期解的充分条件.     

具有无穷时滞中立型泛函微分方程概周期解的存在性

对具有无穷时滞中立型泛函微分方程，本文利用Ｌｉａｐｕｎｏｖ泛函，建立概周期解的存在性定理．     

带无限时滞中立型随机泛函微分方程的解的存在唯一性

In this paper, we will make use of a new method to study the existence and uniqueness for the solution of neutral stochastic functional differential equations with infinite delay (INSFDEs for short) in the phase space BC((?∞,0];Rd). By constructing a new iterative scheme, the existence and uniqueness for the solution of INSFDEs can be directly obtained only under uniform Lipschitz condition, linear grown condition and contractive condition. Meanwhile, the moment estimate of the solution and the estimate for the error between the approximate solution and the accurate solution can be both given. Compared with the previous results, our method is partially different from the Picard iterative method and our results can complement the earlier publications in the existing literatures.     

Controllability of Neutral Functional Differential and Integrodifferential Inclusions with Infinite Delay

Sufficient conditions are derived for the controllability of neutral functional differential and integrodifferential inclusions with infinite delay in a Banach space. The results are obtained by using a fixed-point theorem for condensing maps due to Martelli. An example is given to illustrate the results.     

无界时滞中立型随机微分方程解的矩估计

本文探讨了一类无界时滞的中立型随机微分方程,给出了保证所讨论的方程的整体解存在的条件,并且得到解的某种矩估计.     

具无限时滞的中立型随机泛函微分方程解的存在唯一性

The main aim of this paper is to establish the existence-and-uniqueness theorem for neutral stochastic functional differential equations with infinite delay at phase space BC（（-∞, 0]; R^n） An example is given for illustration.     

Controllability of impulsive neutral functional differential inclusions with infinite delay

The paper is concerned with the controllability of the first-order impulsive neutral functional differential inclusions with infinite delay in a Banach space. Sufficient conditions for controllability are obtained by using a fixed point theorem for condensing maps due to Martelli. As an application, we also consider an impulsive neutral partial functional differential equation.     

非线性中立型随机延迟微分方程随机θ方法的稳定性

本文研究非线性中立型随机延迟微分方程随机θ方法的均方稳定性.在方程解析解均方稳定的条件下,证明了如下结论:当θ∈[0,1/2)时,随机θ方法对于适当小的时间步长是均方稳定的;当θ∈[1/2,1]时,随机θ方法对于任意步长都是均方稳定的.数值结果验证了所获结论的正确性.     

一类具无穷时滞泛函微分方程的周期解

讨论具有无穷时滞中立型泛函微分方程$ \frac{\rm d}{{\rm d}t}\left(x(t)-\int_{-\infty}^{0}g(s,x(t+s)){\rm d}s\right) =A(t,x(t))x(t)+f(t,x_t)$的周期解问题,利用重合度理论中的延拓定理得到了周期解的存在性和唯一性条件;特别地,当$g(s,x)\equiv 0, A(t,x)=A(t)$时, 给出了存在唯一稳定周期解的条件.     

具无限时滞中立型泛函微分方程解的稳定性与有界性

以相空间为基础，研究了具有无限时滞中立型泛函微分方程解的稳定性和有界性，建立了方程解为一致稳定，一致渐近稳定的充要性判据；证明了当方程右端泛函满足Lipschitz条件时，解的一致渐近稳定性蕴涵了有界解的存在性，推广了文献［4-6］中已有的相关结果.     

无限时滞的非线性随机泛函微分方程

本文考虑了无限时滞的非线性随机泛函微分方程,作者在局部利普希茨条件和非线性增长条件下证明了全局解的存在唯一性,矩指数稳定性和渐近稳定性.     

带分布时滞中立型微分方程正解的存在性

主要运用Banach压缩映像原理,研究了分布时滞中立型微分方程ddty(t)+∫abP(t,θ)y(t-θ)dθ+∫cdQ(t,θ)y(t-θ)dθ=0正解的存在性问题,获得了正解存在的充分条件,推广了相关文献的结果.     

具无限时滞线性中立型泛函微分方程周期解

本文证明了具无限时滞D算子型线性中立型泛函微分方程存在周期解当且仅当存在有界解,推广了MasseraJ．L,ChowS．N．和MakayM．的结果．     

Existence Results for Functional Differential Inclusions with Infinite Delay

The aim of the present paper is to investigate the existence of solutions to functional differential inclusions with infinite delay in Banach spaces. A relevant set of phase space axioms is proposed. The main tools used in this paper are certain fixed point theorems based on the setcontraction theory.     

Approximate Controllability of Fractional Impulsive Partial Neutral Stochastic Differential Inclusions with State-Dependent Delay and Fractional Sectorial Operators

In this article, the approximate controllability of fractional impulsive partial neutral stochastic differential inclusions with state-dependent delay and fractional sectorial operators in Hilbert spaces is studied. By using the stochastic analysis, the fractional sectorial operators and a fixed point theorem for multi-valued maps combined with approximation techniques, we discuss a new set of su?cient conditions for the approximate controllability of the systems under the mixed Lipschitz and Carathéodory conditions. An example is provided to illustrate the obtained theory.