STABILITY OF DELAY DIFFERENCE EQUATIONS IN BANACH SPACES

1 IntroductionDiscrete reaction--diffusion type partial difference equations llave recentlybeen introduced by a number of authors as modeIs for the study of spatiotem-poral chaos (see e.g. [2,3j). Stability criteria have also been derived fOr suchequatioIls which invoIve two time-level processes (see e.g. [1l) as well as three-level processes (see e.g. [9]). In this paper, we will study no11linear three--levc1partia1 diffcrence equations in an abstract setting and derive stability criteriafo…     

EXPONENTIAL STABILITY OF LINEAR TIME－VARYING IMPULSIVE DIFFERENTIAL SYSTEMS WITHDELAYS

ＥＸＰＯＮＥＮＴＩＡＬＳＴＡＢＩＬＩＴＹＯＦＬＩＮＥＡＲＴＩＭＥ－ＶＡＲＹＩＮＧＩＭＰＵＬＳＩＶＥＤＩＦＦＥＲＥＮＴＩＡＬＳＹＳＴＥＭＳＷＩＴＨＤＥＬＡＹＳ￥ＧｕａｎＺｈｉｈｏｎｇ（关治洪）；ＬｉｕＹｏｎｇｑｉｎｇ（刘永清）（ＳｏｕｔｈＣｈｉｎａＵｎ...     

ON THE GENERALIZED RESOLVENT OF LINEAR PENCILS IN BANACH SPACES

Utilizing the stability characterizations of generalized inverses of linear operator, we investigate the existence of generalized resolvent of linear pencils in Banach spaces. Some practical criterions for the existence of generalized resolvents of the linear pencil λ→ T λ S are provided and an explicit expression of the generalized resolvent is also given. As applications, the characterization for the Moore-Penrose inverse of the linear pencil to be its generalized resolvent and the existence of the generalized resolvents of linear pencils of finite rank operators, Fredholm operators and semi-Fredholm operators are also considered. The results obtained in this paper extend and improve many results in this area.     

Banach空间中渐近拟非扩张型映象迭代序列的稳定性

本文研究了一类涉及渐近拟非扩张型映象的带误改进Mann迭代序列,利用Tan和Xu的不等式,得到了该带误差Mann迭代序列的稳定性,推广了其他人的结果.     

线性常微分方程系统的稳定性

本文用矩阵的Lozinskii测度的方法,得到了线性常微分方程系统的某些稳定性准则.导出了关于线性系统x'=A(t)x稳定性的充要条件.对于A是常数或周期矩阵的情形,我们的结果与从Jordan标准型和Floquet理论得到的经典结论相同.     

线性常微分方程系统的稳定性

本文用矩阵的Lozinskii测度的方法,得到了线性常微分方程系统的某些稳定性准则.导出了关于线性系统χ'=A(t)χ稳定性的充要条件.对于A是常数或周期矩阵的情形,我们的结果与从Jordan标准型和Floquet理论得到的经典结论相同.     

THE MINIMAL PROPERTY OF THE CONDITION NUMBER OF INVERTIBLE LINEAR BOUNDED OPERATORS IN BANACH SPACES

In this paper we show that in error estimates, the condition number k(T) of any in-vertible linear bounded operator T in Banach spaces is minimal. We also extend the Hahn-Ba-nach theorem and other related results.     

ROBUST GLOBAL EXPONENTIAL STABILITY OF UNCERTAIN IMPULSIVE SYSTEMS

By using the quasi-Lyapunov function, some sufficient conditions of global exponential stability for impulsive systems are established, which is the basis for the following discussion. Then, by employing Riccati inequality and Hamilton-Jacobi inequality approach, some sufficient conditions of robust exponential stability for uncertain linear/nonlinear impulsive systems are derived, respectively. Finally, some examples are given to illustrate the applications of the theory.     

二维广义Ginzburg-Landau方程在Banach空间的指数吸引子

本文应用能量积分和解析半群的有关估计,研究广义二维Ginzburg-Landau方程 在Banach空间LP(Ω)的子空间X-α的指数吸引子.     

HILBERT空间中散逸动力系统一般线性方法的散逸稳定性

１．引言 １９９４年,Ｓｔｕａｒｔ与 Ｈｕｍｐｈｒｉｅｓ［４,５］首先考察了用 Ｒｕｎｇｅ－Ｋｕｔｔａ方法求解 Ｒｍ中的散逸动力系统（２．１）－（２．２）时数值解是否继承真解具有的散逸稳定性,并表明代数稳定且不可约的 Ｒｕｎｇｅ－Ｋｕｔｔａ方法是散逸稳定的且有一有界吸引集．１９９６年,本文作者［１］把这一工作推广到了两类特殊的一般线性方法．１９９７年,Ｈｉｌｌ在［３］中证明了Ａ－稳定是单支方法散逸稳定的充要条件,在［２］中又把文［４,５］的工作推广到了 Ｈｉｌｂｅｒｔ空间中的散逸动力系统（２．１）－（…     

RANDOMLY CONNECTED DYNAMICAL SYSTEMS ON BANACH SPACES

We give sufficient conditions for asymptotic stability of Markov operators governing the evolution of measures due to the action of randomly chosen dynamical systems on Banach spaces. We show that the existence of an invariant measure for the transition operator implies the existence of an invariant measure for a semigroup generated by the considered systems.     

EXPONENTIAL STABILITY FOR A CLASS OF SWITCHED STOCHASTIC SYSTEMS

In this paper, the stability properties for a class of switched stochastic systems with commutative componentwise subsystem matrices are studied. Under some switching law, the trivial solutions of the above systems are proved to be exponentially stable in mean square and almost sure exponentially stable if the random perturbations are sufficiently "small".     

DISJOINTNESS OF OPERATOR RANGES IN BANACH SPACES

Abstract

Let X be a Banach space. A linear subspace of X is called an operator range if it coincides with the range of a bounded linear operator defined on some Banach space. The paper studies disjointness and inclusion properties of various types of operator ranges in a separable infinite dimensional Banach space X. One of the main results is the following: Let E be a non-closed operator range in X. Then X contains a non-closed dense operator range R with the properties E∩= {0}, and R is decomposable, i.e. R = M + N where M,N are closed and infinite dimensional and M ∩ N = {0} (Theorem 6.2).     

一阶广义分布参数系统的指数稳定性

利用退化半群的方法讨论了Hilbert空间中一阶广义分布参数系统的指数稳定性,并给出了判断指数稳定性的充要条件.     

ON ORBITS OF POLYNOMIAL MAPS IN BANACH SPACES

Abstract

We obtain some results concerning the notions of hypercyclicity and supercyclicity for continuous homogeneous polynomial maps in Banach spaces. We also present a generalization of a theorem due to Beauzamy concerning the existence of orbits tending to infinity for continuous linear operators with spectral radius > 1.     

A NEW PERTURBATION THEOREM FOR MOORE-PENROSE METRIC GENERALIZED INVERSE OF BOUNDED LINEAR OPERATORS IN BANACH SPACES

In this paper,we investigate a new perturbation theorem for the Moore-Penrose metric generalized inverses of a bounded linear operator in Banach space. The main tool in this paper is "the generalized Neumann lemma" which is quite different from the method in [12] where "the generalized Banach lemma" was used. By the method of the perturbation analysis of bounded linear operators,we obtain an explicit perturbation theorem and three inequalities about error estimates for the Moore-Penrose metric generalized inverse of bounded linear operator under the generalized Neumann lemma and the concept of stable perturbations in Banach spaces.     

一类线性微分代数系统的稳定性

本文讨论了一类线性时变微分代数系统的稳定性.利用Rosenbrock系统受限等价性理论,直接由方程系数给出了一些稳定性的充分条件.     

Banach空间中的相补问题

本文在Ｂａｎａｃｈ空间中研究了三类相补问题解的存在性。所得结果是［４，５，６，９，１１－１４］中相应结果的深入和发展。     

THE STABILITY OF LINEAR MULTISTEP METHODS FOR LINEAR SYSTEMS OF NEUTRAL DIFFERENTIAL EQUATIONS

1. IntroductionFor a large class of electrical ~ks containing IOssless transmission lines the describingequations can be reduced to a system of neutral differential equations.This paper deals with the numerical solution of initial value problems for syste…