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唯一性

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By the method in this paper,for deciding the global asymptotic stability of the equilibrium point,it is not necessary to verify whether the equilibrium point is unique and to construct Liyapunov functions.

与目前该问题所采用的LIYAPUNOV直接法相比,该方法具有无须判断平衡点的唯一性,判别方程直接明了等优点,电路维数越大时,本文的方法越有其优势。

Thirdly, by using the differential inequalities method, the existence, uniqueness and its asymptotic behavior of solution for the problem are studied.

然后,利用微分不等式方法,研究了问题解的存在、唯一性和渐近性态。

Firstly,the stability and uniqueness of limit cycles of a kind of autonomous nonlinear dynamical system is discussed.

讨论了一类自治系统极限环的唯一性与稳定性。

Firstly, we prove the existence and uniqueness of the adapted solution of multi-dimensional backward stochastic differential equations driven by Brownian motion and Lévy process by using predictable representation theorem and the fixed point theorem about contract mapping, and also prove the comparison theory.

第一部分运用可料表示定理和压缩映射原理证明由布朗运动和Lévy过程共同驱动的多维倒向随机微分方程适应解的存在唯一性及其相应的比较定理。

Huang and Lin proposed the weak solution concept for Backward Stochastic Differential Equation This paper based on the predecessor's work , gives the weak solution concept for Backward Stochastic Differential Equation with continuous martingale,uses the Girsanov transformation, obtains its weak solution of the existence of a necessary and sufficient conditions, and on this basis obtains its weak solution of the existence of sufficient conditions,these sufficient conditions weakened the drifting coefficient which requested in the existence uniqueness of strong solution to satisfy the Lipschitz condition the request.

本文在前人研究的基础上,给出由连续鞅驱动的倒向随机微分方程弱解的概念,利用Girsanov变换,得到其弱解存在的存在的一个充分必要条件,并在此基础上得到了其弱解存在的一些充分条件,这些充分条件减弱了在强解的存在唯一性中要求的漂移系数满足Lipschitz条件的要求。

Secondly, we consider stochastic LQ optimal control problem driven by Lévy processes and Brownian motion. By applying the -Lévy formula, Gronwall's inequality, Young's inequality and Cauchy-Schwarz inequality, we obtain the closeness property of the solution of multi-dimensional backward stochastic Riccati differential equations.

第二部分首先研究由布朗运动和Lévy过程共同驱动的随机LQ最优控制问题,接着利用-Lévy公式、Gronwall不等式、Young不等式及Cauchy-Schwarz不等式证明多维倒向随机Riccati微分方程适应解的闭性质,并利用此性质证明一维BSRDE解的存在唯一性

For a given strictly proper rational function matrix over a commutative Banach algebra, the controllable, observable realizations have been constructed, the uniqueness of minimal realizations under the system equivalence has been proved, also, the necessary and sufficient conditions for decoupling have been given.

对给定的定义在交换Banach代数上的严格真有理函数矩阵,构造了可控型、可观型的实现,证明了其极小实现在系统等价意义下的唯一性;给出了交换B.fi。

The purpose of this part is to study the delay differential systems in Banach space using the method of fixed point theorem.

一方面在非时滞的情况下通过构造比较函数,利用Brouwer不动点定理得到非时滞微分方程正周期解的存在唯一性,及周期解全局吸引的充分条件。

In this paper a class integral differential equation on Banach space is studied.Existence,uniqueness and regularity of mild solutions are proved.

研究了Banach空间上的一类非线性脉冲积微分方程温和解的存在唯一性以及其正则性。

In chapter 1, firstly, by using classical analysis methods, such as the introduction of Bessel function and semigroup theory, we transform the pseudo-parabolic equation into an abstract operator equation and achieve the existence and uniqueness of the local solution.

在第一章中,利用经典的分析方法,引入Bessel势函数,将伪抛物型方程转化为抽象算子方程,首先,利用算子半群理论,论证了局部解的存在唯一性

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