IMPULSIVE BOUNDARY VALUE PROBLEMS FOR STURM-LIOUVILLE TYPE DIFFERENTIAL INCLUSIONS

In this paper, the authors investigate the existence of solutions of impulsive boundary value problems for Sturm-Liouville type differential inclusions which admit non-convex-valued multifunctions on right hand side. Two results under weaker conditions are presented. The methods rely on a fixed point theorem for contraction multi-valued maps due to Covitz and Nadler and Schaefer＇s fixed point theorem combined with lower semi-continuous multi-valued operators with decomposable values.     

On Existence and Uniqueness of Random Impulsive Differential Equations

This paper studies existence and uniqueness for random impulsive differential equations. The authors first generalize a random fixed point theorem of Schaefer’s type. Then the authors shall rely on the generalized Schaefer’s type random fixed point theorem to discuss the existence of the system. In addition, the authors study the existence and uniqueness of random impulsive differential equations by applying random Banach fixed point theorem and obtain some less conservative results. Finally, an example is given to illustrate the effectiveness of the results.     

Existence and Stability for Periodic Solution of Cooperation Ecosystem with Diffusion

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Recent progress on controllability/observability for systems governed by partial differential equations

<正> The main purpose of this paper is to overview some recent methods and results on controllability/observability problems for systems governed by partial differential equations.First,the authorsreview the theory for linear partial differential equations,including the iteration method for the nullcontrollability of the time-invariant heat equation and the Rellich-type multiplier method for the exactcontrollability of the time-invariant wave equation,and especially a unified controllability/observabilitytheory for parabolic and hyperbolic equations based on a global Carleman estimate.Then,the authorspresent sharp global controllability results for both semi-linear parabolic and hyperbolic equations,based on linearization approach,sharp observability estimates for the corresponding linearized systemsand the fixed point argument.Finally,the authors survey the local null controllability resultfor a class of quasilinear parabolic equations based on the global Carleman estimate,and the localexact controllability result for general hyperbolic equations based on a new unbounded perturbationtechnique.     

Existence and Stability of Positive PeriodicSolution of Delay Logistic Ecosystem with Feedback Control and Diffusion

1IntroductionWeconsiderthedelaylogisticecosystemwithfeedbackcontrolanddiffusionoftheformConcerningthestabilityproblemofpositivestead-stateforsystem(1.1),ithasbeendiscussedbyX.Shengli[1],whereastheasymptoticbehaviorofsolutionsofsystem(1.1)withoutdiffusionhasalsobeenconsideredbyK.Gopalsamy[2]andtheoscillationofsystem(1.1)withoutdiffusionandfeedbackcontrolcanbefoundinreference[3](K.GopalsamyandG.Ladas),Inreference[4],J.Dangpinghasgivedsufficientconditionsofexistenceandstabilityofperiodicsolut…     

SOME INITIAL-OBLIQUE DERIVATIVE BOUNDARY VALUE PROBLEM FOR QUASILINEAR PARABOLIC EQUATIONS WITH UNBOUNDED COEFFICIENTS

1 IntroductionThis paper is concerned with the a priori estimates and the ekistence of solutions of theinitiaLoblique derivative boundary value problem for quasilinear non-divergence parabolic equa-tions as follows:where O is a bounded domain in R"(N > 2) with smooth boundary 0a e C' ', QT =[o,T) x a be the parabolic domain in H" ,, ST = [o,T) x aa is the lateral boundary, andarQT is the parabolic boundary of QT' The repeated indices means summatiOns from 1 to N.In [11, the first bounda…     

Existence and Stability for Periodic Solution of Competition Reaction－Diffusion Models with Grazing Rates in Population Dynamics

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不确定性下多目标博弈中弱Pareto-NS均衡的存在性

在已知不确定参数变化范围的假设下, 研究了多目标博弈中弱Pareto-NS均衡点的存在性问题. 首先结合非合作博弈中NS-均衡的定义, 给出不确定性下多目标博弈中弱Pareto-NS均衡的定义. 进一步借助Fan-Glicksberg不动点定理, 证明弱Pareto-NS均衡点的存在性. 最后给出算例, 验证其可行性.     

Existence and Uniqueness Results for Quaternion-Valued Nonlinear Impulsive Differential Systems

This paper studies the existence and uniqueness conditions for the quaternion-valued nonlinear impulsive system. Firstly, a space of quaternion-valued piecewise functions is constructed and completeness of the space is also proved. Then by taking advantage of the Bielecki norm and fixed point theorem, existence and uniqueness criteria of quaternion-valued nonlinear impulsive system are obtained. At last, an example is given to illustrate our theoretical results.     

Almost Automorphic Solutions for Quaternion-Valued Hopfield Neural Networks with Mixed Time-Varying Delays and Leakage Delays

This paper considers a class of quaternion-valued Hopfield neural networks with mixed time-varying delays and leakage delays. By utilizing the exponential dichotomy of linear differential equations, Banach's fixed point theorem and differential inequality techniques, the authors obtain some sufficient conditions to ensure the existence and global exponential stability of almost automorphic solutions for this class of quaternion-valued neural networks. The results are completely new. Finally,the authors give an example to illustrate the feasibility of the results.     

Exact Controllability and Stabilization of Networkswith an Interior Point Mass

1IntroductionInrecentyears,therehavebeenmanyinterestingtopicsoncontrolandstabilizationofsocalled"hybridsystems"illwhichthedynamicsystemsandpossiblyrigidstructuresarerelatedthroughsomeformsofcouplillg.Forexample,seeII],[2]fornetworksofstringswithillteriorpointmasses,15],I6]forseriallyconnectedbeams,17],[slforbeamswitllelldmasses.Thereisseriouserrorinwork[l]becausesystem(l.l)illif]isnotm-dissipativeaccordillgtotheenergynormal(l.3)ll].Inthisarticle,wecorrectthemodelof[l]alldgiveanewenergynormal…     

损失厌恶型n人非合作博弈Nash均衡

基于参与人是完全理性的期望效用理论是分析经典非合作博弈问题的基本理论,然而越来越多的研究表明,博弈中的参与人往往呈现出有限理性的特点.本文考虑有限理性参与人具有损失厌恶的行为特点,并对此类n人非合作博弈的Nash均衡进行详细研究.首先,根据参与人损失厌恶的行为特点,设置了n人非合作博弈安全水平参照点,并证明此参照点存在且唯一.然后,基于该参照点定义了竹人非合作博弈的损失厌恶Nash均衡,借助Brouwer不动点定理证明了该博弈均衡的存在.最后利用算例进行分析和验证,结果表明参与人的损失厌恶行为会对博弈的均衡策略产生影响,同时参与人的支付效用也会随之发生变化.     

Approximate Controllability for Degenerate Heat Equation with Bilinear Control

This paper investigates the nonnegative approximate controllability for the one-dimensional degenerate heat equation governed by bilinear control. Both non-controllability and approximate controllability are studied for the system. If the control is restricted to act on a fixed domain, it is not controllable. If the control is allowed to mobile, it is approximately controllable.     

Existence of Positive Periodic Solutions of Competitor-Competitor-Mutualist Lotka-Volterra Systems with Infinite Delays

In this paper,the authors primarily explore a delayed competitor-competitor-mutualist Lotka-Volterra model,which is a system of differential equation with infinite integral.The authors first study the existence of positive periodic solutions of the model by using the Krasnoselskii’s fixed point theorem,and then present an example to illustrate the main results.     

ON THE NUMBER OF FIXED POINTS OF NONLINEAR OPERATORS AND APPLICATIONS

In this paper, the famous Amann three-solution theorem is generalized. Multiplicity question of fixed points for nonlinear operators via two coupled parallel sub-super solutions is studied. Under suitable conditions, the existence of at least six distinct fixed points of nonlinear operators is proved. The theoretical results are then applied to nonlinear system of Hammerstein integral equations.     

Controllability of Singular Distributed Parameter Systems in the Sense of Mild Solution

Necessary and sufficient conditions for the exact controllability and approximate controllability of a singular distributed parameter system are obtained. These general results are used to examine the exact controllability and approximate controllability of the Dzektser equation in the theory of seepage.     

Reachability/controllability of high order mix-valued logical networks

This paper addresses the reachability/controllability of high order mix-valued logical control networks by using the semi-tensor product method, and presents some necessary and sufficient conditions for the reachability/controllability. The high order mix-valued logical network is converted into an algebraic form first, based on which the reachability/controllability of the system is then investigated, and several necessary and sufficient conditions are established. The study of several illustrative examples shows that our new method is very effective in dealing with the reachability/controllability of high order mix-valued logical control networks.     

二维广义系统Roesser模型局部能达和局部能控性

研究了二维广义系统Roesser模型的性质,推导出了该系统的状态响应公式.给出了其在矩形区域上局部能达和局部能控的充分必要条件.同时,利用二维Z变换理论,给出了二维广义系统Roesser模型局部能达和局部能控的等价定义,并得出该模型相应的局部能达和局部能控的新的充分必要条件.     

二阶积-微分方程奇异边值问题解的存在性

讨论了一类二阶积 微分方程两点边值问题解的存在性。该问题以四阶微分方程两点边值问题为特例。首先在不假设非线性项单调,并允许其有奇性的情况下,利用上下解方法与Schauder不动点定理,获得了二阶Fredholm型积 微分方程两点边值问题解的存在性结果,然后把该结果应用于两端简单支撑的弹性梁的平衡状态模型—四阶微分方程边值问题。     

Controllability and observability of networked control systems with time-varying delays

The controllability and observability of networked control systems are studied. Aiming at the networked control system with time-varying delay, the sufficient and necessary conditions for complete controllability and complete observability of the system are presented, respectively. Because of Markov characteristic of the network-induced delay, in terms of stochastic theory, a sufficient and necessary condition for completely mean value controllability of networked control systems is obtained. Further, the conditions that the controllability and observability of networked control systems are equivalent to the initial time-invariant system are given. Controllability and observability realization indexes are also discussed, respectively. The numerical example demonstrates the effectiveness of the proposed theory.