Periodic Solutions for a Class of Neutral Functional Differential Equations with Distributed and Discrete Delays

Based on Krasnoselskii's fixed point theorem,matrix measure and functional analysis methods,some new sufficient conditions for the existence of periodic solutions of neutral functional differential equations with distributed and discrete delays are obtained. Moreover,we construct an example to illustrate the feasibility of our results.

EXISTENCE OF SOLUTION AND APPROXIMATE CONTROLLABILITY OF A SECOND-ORDER NEUTRAL STOCHASTIC DIFFERENTIAL EQUATION WITH STATE DEPENDENT DELAY

This paper has two sections which deals with a second order stochastic neutral partial differential equation with state dependent delay. In the first section the existence and uniqueness of mild solution is obtained by use of measure of non-compactness. In the second section the conditions for approximate controllability are investigated for the distributed second order neutral stochastic differential system with respect to the approximate controllability of the corresponding linear system in a Hilbert space. Our method is an extension of co-author N. Sukavanam’s novel approach in [22]. Thereby, we remove the need to assume the invertibility of a controllability operator used by authors in [5], which fails to exist in infinite dimensional spaces if the associated semigroup is compact. Our approach also removes the need to check the invertibility of the controllability Gramian operator and associated limit condition used by the authors in [20], which are practically difficult to verify and apply. An example is provided to illustrate the presented theory.

Exponential Stability of Impulsive Neutral Stochastic Functional Differential Equations with Markovian Switching

The aim of this paper is to the discussion of the exponential stability of a class of impulsive neutral stochastic functional differential equations with Markovian switching.Under the influence of impulsive disturbance,the solution for the system is discontinuous.By using the Razumikhin technique and stochastic analysis approaches,as well as combining the idea of mathematical induction and classification discussion,some sufficient conditions for the pth moment exponential stability and almost exponential stability of the systems are obtained.The stability conclusion is full time-delay.The results show that impulse,the point distance of impulse and Markovain switching affect the stability for the system.Finally,two examples are provided to illustrate the effectiveness of the results proposed.

The Existence and Uniqueness of the Solution for Neutral Stochastic Functional Differential Equations with Infinite Delay

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.

Stability Criteria of Nonlinear Impulsive Differential Equations with Infinite Delays

In this paper, we consider the uniform stability and uniformly asymptotical stability of nonlinear impulsive infinite delay differential equations. Instead of putting all components of the state variable x in one Lyapunov function, several Lyapunov-Razumikhin functions of partial components of the state variable x are used so that the conditions ensuring that stability are simpler and less restrictive; moreover, examples are discussed to illustrate the advantage of the results obtained.

Well-Posedness and Exponential Estimates for the Solutions to Neutral Stochastic Functional Differential Equations with Infinite Delay

In this work,neutral stochastic functional differential equations with infinite delay(NSFDEw ID)have been addressed.By using the Euler-Maruyama scheme and a localization argument,the existence and uniqueness of solutions to NSFDEw ID at the state space Cr under the local weak monotone condition,the weak coercivity condition and the global condition on the neutral term have been investigated.In addition,the L2 and exponential estimates of NSFDEw ID have been studied.

The Existence and Uniqueness for the Solution of Neutral Stochastic Functional Differential Equations with Infinite Delay

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.

EXISTENCE RESULTS FOR IMPULSIVE NEUTRAL EVOLUTION DIFFERENTIAL EQUATIONS WITH STATE-DEPENDENT DELAY

This paper is mainly concerned with the existence of mild solutions to a first order impulsive neutral evolution differential equations with state-dependent delay. By suitable fixed point theorems combined with theories of evolution systems,we prove some existence theorems. As an application,an example is also given to illustrate the obtained results.

STABILITY OF NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAY

In the phase space （Ch,│·│h）, by using the Liapunov functional approach, sufficient and necessary criteria for the uniform stability and uniformly asymptotic stability of solutions to neutral.functional differential equations with infinite delay are established. We also prove that the uniformly asymptotic stability of the solutions implies the existence of the bounded ones.

UNIFORM ASYMPTOTIC STABILITY OF SOLUTIONS TO NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAY

In this paper, we consider neutral functional differential equations with infinite delay. Sufficient and necessary criteria for the g-uniform asymptotic stability of solutions to the system in the phase space (Cg,|·|g) are established.

EXISTENCE OF MILD SOLUTIONS TO NEUTRAL FRACTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAY

In this paper, we consider the existence of mild solution to a class of neutral fractional differential equations with infinite delay. By means of fixed points methods, we obtain some sufficient conditions for the existence and uniqueness of mild solutions, which extend some known results.

STABILITY AND ALMOST PERIODIC SOLUTIONS OF NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAY

For the operator D(t), we prove the inherence theorem, Theorem 2. Basing on it, we study the stability with respect to the hull for neutral functional differential equations with infinite delay. We prove that if periodic Eq.(1) possesses the solution ξ(t) that is uniformly asymptotically stable with respect to then Eq.(1) has an mω-periodic solution p(t), for some integer m≥1. Furthermore, we prove that if the almost periodic Eq.(1) possesses the solution ξ(t) that is stable under disturbance from H+ (ξ,D,f), then Eq.(1) has an almost periodic solution.

OSCILLATION THEOREM TO SYSTEMS OF IMPULSIVE NEUTRAL DELAY PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS

In this paper, we study the oscillation of solutions to the systems of impulsive neutral delay parabolic partial differential equations. Under two different boundary conditions, we obtain some sufficient conditions for oscillation of all solutions to the systems.

EXISTENCE OF SOLUTION TO NONLINEAR SECOND ORDER NEUTRAL DIFFERENTIAL SYSTEM WITH DELAY

This paper is concerned with the existence of solution to nonlinear second order neutral differential equations with infinite delay in a Banach space. Sufficient conditions for the existence of solution are obtained by a Schaefer fixed point theorem.

无穷时滞泛函微分方程的概周期解

讨论一类高维的具无穷时滞的中立型泛函微分方程的概周期解问题。利用 Ch 空间,矩阵测度 和 Krasnoselskii 不动点定理获得了其概周期的存在性与唯一性定理。同时给出了模包含关系, 推广了相应文献的结果。

无限时滞一阶脉冲中立型偏泛函微分方程温和解的存在性

利用Krasnoselski-Schaefer型不动点理论,讨论了形如:d/dt[x(t)-g(t,xt)]=Ax(t)+f(t,xt)的无限时滞一阶脉冲中立型偏泛函微分方程温和解存在性问题.

无穷时滞的一阶脉冲偏中立型泛函微分方程积分解的存在唯一性

利用积分半群算子理论结合Banach压缩映射原理,证明了一类无穷时滞的一阶中立型脉冲偏泛函微分方程积分解的存在唯一性和连续依赖性.

一类0<α<1带有无限时滞的中立型脉冲微分方程mild解的存在性（英文）

本文研究了一类0<α<1带有无限时滞的中立型脉冲微分方程mild解的存在性的问题.利用解算子的相关性质及M(o|¨)nch不动点理论的方法,获得了这类方程的mild解并予以证明,且得到了解的存在性的结果.

脉冲无穷时滞中立型测度微分方程mild解的存在性

该文主要研究无穷时滞脉冲中立型测度微分方程mild解的存在性.在半群非紧的条件下,通过运用算子半群理论、Kuratowski非紧性测度、Mönch不动点定理及分段估计的方法得出方程mild解存在的充分条件.没有使用先验估计和非紧性限制条件,推广许多已有的结果.最后,给出一个实例说明结果的可行性.

无限滞后脉冲测度微分方程解对参数的连续依赖性

本文研究了解对参数连续依赖性的问题.利用Kurzweil-Stieltjes积分理论和正则函数的相关性质,获得了无限滞后脉冲测度微分方程解对参数的连续依赖性的结果.