共查询到20条相似文献,搜索用时 15 毫秒
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利用拓扑度理论和不动点指数理论,研究了二阶非线性变系数奇异微分方程u″(t)+a(t)u(t)=r(t)f(u(t))的周期解的存在性.特别地,本文没有假设a(t)和f(u)的非负性. 相似文献
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讨论了一四阶具有双参数的弱非线性方程在有限区间上的奇摄动边值问题.在一定的假设下,首先,利用幂级数形式展开方法,构造了原问题的外部解A·D2其次,利用伸长变量,在左端点附近构造问题解的第一边界层校正项.然后,利用更强的伸长变量,仍然在左端点附近构造问题解的第二边界层校正项.第二边界层的厚度比第一边界层的厚度更小,形成在左端点附近的边界层的套层.最后利用微分不等式理论,证明了边值问题解的存在性、和在整个区间内一致有效性和渐近性态,得到了满意的结果. 相似文献
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The authors study the existence of mild solutions to a functional differential equation with delay and random effects. They use a random fixed point theorem with a stochastic domain. An example is included to illustrate their results. 相似文献
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基于可信性理论,将提出一类带有模糊参数的运输期望值模型.然后,讨论模糊运输期望值模型的基本性质.最后,给出一个数值例子来表明所设计模型的实用性. 相似文献
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A.R.ELAMROUSS 《数学学报(英文版)》2005,21(1):129-142
This paper contains a generalization of the well-known Palais-Smale and Cerami compactness conditions. The compactness condition introduced is used to prove some general existence theorems for critical points. Some applications are given to differential equations. 相似文献
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Z. Huang V. Chandra S. Jiang R. Kumar 《Mathematical and Computer Modelling of Dynamical Systems: Methods, Tools and Applications in Engineering and Related Sciences》2013,19(3):233-254
Obtaining accurate models of systems which are prone to failures and breakdowns is a difficult task. In this paper we present a methodology which makes the task of modeling failure prone discrete event systems (DESs) considerably less cumbersome, less error prone, and more user-friendly. The task of obtaining commonly used automata models for DESs is non-trivial for most practical systems, owing to the fact that the number of states in the commonly used automata models is exponential in the number of signals and faults. In contrast a model of a discrete event system, in the rules based modeling formalism proposed by the co-authors of this paper, is of size polynomial in the number of signals and faults. In order to model failures, we augment the signals set of the rules based formalism to include binary valued fault signals, the values representing either a non-faulty or a faulty state of a certain failure type. Addition of new fault signals requires introduction of new rules for the added fault signal events, and also modification of the existing rules for non-fault events. The rules based modeling formalism is further extended to model real-time systems, and we apply it to model delay-faults of the system as well. The model of a failure prone DES in the rules based can automatically be converted into an equivalent (timed)-automaton model for a failure analysis in the automaton model framework. 相似文献
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研究了具有Seikkala导数的n阶模糊微分方程的模糊初值问题,通过1-水平截集方程和左、右扩展方程的解构造出原模糊微分方程的解,给出了具体的算例. 相似文献
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We consider the construction of Dirichlet series for quasilinear partial differential equations. We obtain a remarkable result that for the class of equations under study, the only equations that admit such a series solution are transformable back onto the only known integrable equation within the class. 相似文献
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讨论了怎样快速求出Fuzzy关系方程干解的方法.探讨了该方法在模糊在线控制系统中的应用,同时给出了如何快速构建经济适用的动态模糊控制器的设计方法. 相似文献
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综述随机偏微分方程的基本概念、理论、方法与应用,内容包括Hilbert空间中的Wiener过程、Ito随机积分、随机偏微分方程的解及其有效动力学。还介绍了随机偏微分方程的粗糙轨道、正则结构以及在Kardar-ParisiZhang(KPZ)方程中的应用。还介绍了段金桥与王伟的著作《Effective Dynamics of Stochastic Partial Differential Equations(随机偏微分方程的有效动力学)》的基本内容。 相似文献
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流形上微分方程的算法 总被引:1,自引:0,他引:1
流形上微分方程的数值方法,是近十多年发展起来的、当前热门的数值方法.特别是所谓的的李群方法是在动力学问题的需求下诞生的,它能在弯曲的空间中进行离散化,根本不会出现‘违约问题’.人们将它应用到动力学方程模型等,取得了不少成果,应用前景看好.它的出现可以说是20世纪数值数学领域的新成就.本文主要介绍这一新的理论,并提出了许多急待解决的新的课题. 相似文献
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阮保庚 《数学物理学报(A辑)》1999,19(3):313-317
构造了仅由两个参量确定的方法类RK,(μ,δ),一切节点属于区间[0,1]且至少2s-1阶相容的s级RK的方法,如Radau|A,Radau||A,Gauss方法等,均是其特例.此类方法的代数稳定性与A-稳定性均等价于参量的μ的非负性,这一准则改进了Burrage的如下结论:一个满足简化条件B(s)和C(s)的s级RK的方法代数稳定的必要条件是它至少2s—1阶相容.基于此类方法构造了高阶指数拟合的RK公式,且公式是代数稳定的,因而适于求解非线性stiff问题.特别,当用k(k>1)步方法求解stiff问题时,用拟会得当的RK公式确定k-1个附加初值是行之有效的. 相似文献
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运用动力系统定性理论,提出一种分析非线性方程解的方法,从而可以避免求解的繁琐过程,得到非线性方程解的几何形态.此方法特别适合于分析难以求出精确解的方程. 相似文献
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We study the limit properties of solutions to one class of systems of differential equations as the number of equations and some parameters tend to infinity. We establish a close connection between solutions to these systems and differential equations with retarded argument. Our convergence theorems provide a new method for approximation of solutions to nonlinear differential equations with retarded argument.Original Russian Text Copyright © 2005 Demidenko G. V. and Likhoshvai V. A.The authors were supported by the Russian Foundation for Basic Research (Grants 03-01-00328, 03-04-48506, 03-04-48829, 03-07-96833, 04-01-00458, 05-04-49068, and 05-07-90274), the Integration Grant of the Siberian Branch of the Russian Academy of Sciences (No. 119 and 148), the Program Development of the Scientific Potential of Higher School of the Ministry for Education of the Russian Federation (Grant 8273), and NSF:FIBR (Grant EF-0330786).__________Translated from Sibirskii Matematicheskii Zhurnal, Vol. 46, No. 3, pp. 538–552, May–June, 2005. 相似文献
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