Approximate Controllability of Neutral Functional Differential Systems with State-Dependent Delay

This paper deals with the approximate controllability of semilinear neutral functional differential systems with state-dependent delay. The fractional power theory and α-norm are used to discuss the problem so that the obtained results can apply to the systems involving derivatives of spatial variables. By methods of functional analysis and semigroup theory, sufficient conditions of approximate controllability are formulated and proved. Finally, an example is provided to illustrate the applications of the obtained results.     

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.     

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.     

Optimal Solutions of Fractional Nonlinear Impulsive Neutral Stochastic Functional Integro-Differential Equations

Abstract

In this article, we consider a new class of fractional impulsive neutral stochastic functional integro-differential equations with infinite delay in Hilbert spaces. First, by using stochastic analysis, fractional calculus, analytic α-resolvent operator and suitable fixed point theorems, we prove the existence of mild solutions and optimal mild solutions for these equations. Second, the existence of optimal pairs of system governed by fractional impulsive partial stochastic integro-differential equations is also presented. The results are obtained under weaker conditions in the sense of the fractional power arguments. Finally, an example is given for demonstration.     

Banach空间中一类具阻尼的二阶微分包含的可控性

主要研究了Banach空间一类具有阻尼项的二阶微分包含的可控性,利用集值映射不动点定理,讨论了集值函数取凸值的情况,给出了微分包含可控性的充分条件.     

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.     

Existence of Solution of Nonlinear Neutral Stochastic Differential Inclusions with Infinite Delay

Abstract

This article is concerned with the existence of solution of nonlinear neutral stochastic differential inclusions with infinite delay in a Hilbert Space. Sufficient conditions for the existence are obtained by using a fixed point theorem for condensing maps due to Martelli.     

具有Hille-Yosida算子的非线性随机脉冲泛函微分包含的可控性

本文研究具有Hille-Yosida算子的非线性随机脉冲泛函微分包含的可控性.假设多值非线性和脉冲函数满足由非紧性测度表示的正则性条件,利用非紧性测度理论和多值凝聚不动点定理,得到这类微分包含的可控性的充分条件.     

非线性中立型时滞偏微分方程的振动定理

建立了一类具有连续分布时滞的非线形中立型偏微分方程的若干新的振动定理,我们的结果推广和改进了一些文献中的振动准则.     

Approximate controllability of a fractional stochastic partial integro-differential systems via noncompact operators

Objective: in this article, we discuss the approximate controllability problems of a new class of fractional impulsive stochastic partial integro-differential systems in separable Hilbert spaces. Methods: by applying the fractional calculus, the measure of noncompactness, properties of fractional resolvent operators and fixed point theorems. Results: we prove our main results without the hypotheses of compactness on the operator generated by the linear part of systems. Instead we suppose that the nonlinear term only satisfies a weakly compactness condition. Conclusion: the approximate controllability for the control systems with noncompact operators is established. Finally, an example is given for the illustration of the obtained theoretical results.     

Approximate controllability of second-order impulsive stochastic differential equations with state-dependent delay

In this paper we study a kind of second-order impulsive stochastic differential equations with state-dependent delay in a real separable Hilbert space. Some sufficient conditions for the approximate controllability of this system are formulated and proved under the assumption that the corresponding deterministic linear system is approximately controllable. The results concerning the existence and approximate controllability of mild solutions have been addressed by using strongly continuous cosine families of operators and the contraction mapping principle. At last, an example is given to illustrate the theory.     

不确定中立型线性随机时滞系统的鲁棒稳定性

建立了中立型随机微分时滞方程的LaSalle不变原理,然后应用LaSalle不变原理讨论了不确定中立型随机时滞系统的随机渐近稳定和几乎必然指数稳定的代数判据, 同时给出示例说明结果的有效性．     

带有积分边值条件的分数阶微分包含解的存在性

本文利用Hausdorff非紧测度、分数阶的微积分理论和Kakutani不动点定理,研究了满足条件z(0)=z0,z(1)=λcI0+γ+z(η)=λ∫0η(η-s)γ-1/Γ(γ)z(s)ds的广义Bagley-Torvik型分数阶微分包含cDv1 z(t)-ac Dv2 Z(t)∈F(t,z(t)),t∈(0,1)解的存在性.其中1 0,a和λ是给定的常数.     

Controllability of second‐order impulsive neutral functional differential inclusions in Banach spaces

In this paper, we shall prove the controllability of second‐order impulsive neutral functional differential inclusions with infinite delay in Banach spaces. The results are obtained by using the theory of strongly continuous cosine families and a fixed point theorem for multi‐valued mappings. As an example, we also consider an second‐order impulsive neutral functional differential equation with infinite delay. Copyright © 2009 John Wiley & Sons, Ltd.     

一类具时滞的高阶中立型偏微分方程解的振动性

研究一类具时滞的偶数阶非线性中立型偏微分方程解的振动性,获得了一些新的充分判据,所得结果推广和包含了文[1]及[2]的相应结果.     

Controllability of stochastic semilinear functional differential equations in Hilbert spaces

In this paper approximate and exact controllability for semilinear stochastic functional differential equations in Hilbert spaces is studied. Sufficient conditions are established for each of these types of controllability. The results are obtained by using the Banach fixed point theorem. Applications to stochastic heat equation are given.     

非线性偶阶中立型时滞偏微分方程的振动性

建立了一类非线性偶阶中立型时滞偏微分方程的若干新的振动准则,所得的结果推广和改进了文献中的一些振动结果。     

Controllability of Functional Integro-Differential Inclusions with an Unbounded Delay

In this paper, a sufficient condition is established for the controllability of neutral functional integro-differential inclusions with an unbounded delay in Banach spaces. The approach used is a fixed-point theorem for condensing maps due to Martelli and the theory of analytic semigroup of linear operators. Communicated by F. Zirilli Research supported by NNSF of China, by the Teaching and Research Award Program for Outstanding Young Teachers in Higher Education Institutions of the Ministry of Education of China, and by the Qing Lan Talent Engineering Fund QL-05-164 of Lanzhou Jiaotong University. The authors are grateful to Professor F. Zirilli and two anonymous referees for valuable suggestions improving this paper.     

The Regularity of Stochastic Convolution Driven by Tempered Fractional Brownian Motion and Its Application to Mean-field Stochastic Differential Equations

In this paper, some properties of a stochastic convolution driven by tempered fractional Brownian motion are obtained. Based on this result, we get the existence and uniqueness of stochastic mean-field equation driven by tempered fractional Brownian motion. Furthermore, combining with the Banach fixed point theorem and the properties of Mittag-Leffler functions, we study the existence and uniqueness of mild solution for a kind of time fractional mean-field stochastic differential equation driven by tempered fractional Brownian motion.