查询词典 existence theorem of implicit function

We use the Leggett and Williams fixed point theorem to discuss the existence of three positive solutions for the boundary value problem of second-order nonlinear functional differential equation.

我们使用Leggett和Williams不动点定理讨论了二阶非线性泛函微分方程边值问题的三个正解的存在性。

Lastly, the existence theorem of three positive solutions for the boundary value problem of second-order singular functional differential equation be established by applying the index theory of fixed points in a cone.

最后，我们应用锥上的不动点指标理论建立了二阶非线性奇异泛函微分方程边值问题的三个正解的存在性定理。

This paper discusses a new generalized Quasi-vector variational inequality problem of Gateaux differential mappings in Banach space and proves the existence of a solution for such a problem by the KKM theorem.

研究了Banach空间中一类G-可导映射的广义拟向量变分不等式问题，运用KKM定理证明这类问题解的存在性，并在适当的条件下证明了此类问题与Konnov I V和Yao J C等人提出的广义向量变分不等式问题是等价的。

Supposing the nonlinear term bounded, by using homotopy invariance theorem, we proved the existence of solutions of boundary value problems for a class of nonlinear ordinary differential equations.

在假设一类常微分方程边值问题中的非线性项有界的条件下，运用同伦映射不变性定理，得出了解的存在性结论。

By using the continuation theorem of coincidence degree theory, homotopy invariance property and Lyapunov's approach, some sufficient conditions ensuring the existence and stability of positive periodic solutions of the system are obtained.

利用Mawhin重合度理论，并结合同伦不变性质，以及Lyapunov方法，获得该系统正周期解的存在性和全局稳定性的充分条件，推广和改进最近一些文献的结果。

The existence of positive solutions of some fourth-order singular semi-positone boundary value problems are obtained on a special cone by using the fixed point index theorem.

本文在一个特殊锥上利用不动点指数定理，得到了一类四阶奇异半正边值问题正解的存在性，并给出了一个例子作为对所获结果的应用，推广和改进了一些已知结果。

Some conditions for weakly Persistence and extinction are obtained;In the second part, we respectively use C_h space and C_g space theorem to study the existence of periodic solutions of Lotka-Volterra equation with infinite delay, in the end we get the condition of the existense of periodic solutions and estimate the interzone of it.

第二部分利用相空间理论，分别以C_h空间和C_g空间为相空间研究了具有无限时滞的Lotka-Volterra方程周期解的存在性问题，给出了周期解存在的充分条件，并估计出了周期解的存在区间。

At first, we present a necessary condition for the existence of optimal linear state feedback control by means of Lagrange multiplier theorem.

首先利用Lagrange multiplier定理得到了存在最优线性状态反馈解的必要条件，而在加强的条件下也得到了最优控制存在的充分条件。

On the basis of introducing the fixed point of Banach theorem, this paper firstly elaborates the important application of the existence of the solution of the linear algebraic equation and the ordinary differential equation, then it narrates the important application of obtaining the leading Newton repetitive process and the natural number the inferior square root and the equation root in the approximate calculation.

本文在介绍Banach不动点定理的基础上，首先阐述了其在线形代数方程、常微分方程解的存在性中的重要应用；然后讲述了其在求导Newton迭代法、求自然数的次平方根、求方程根的近似计算中的重要应用；最后，介绍了其在求一类递推数列极限中的应用。

By applying game theory and contraction mapping theorem, a sufficient condition for the existence and uniqueness of Nash equilibrium in a multi-person non-cooperative game is proposed. Another implication in the sense of game theory is presented for the stability condition of supply-demand equilibrium in traditional economic theory. It can demonstrate the stability condition for supply-demand equilibrium in economic theory. So the stable supply-demand equilibrium of cobweb model in economics is in fact equivalent to the Nash equilibrium in game theory. That is a brand-new explanation for the conclusion in traditional economic theory.

应用博弈论中的有关理论与压缩映象定理寻求一类多ISP非合作对策纳什均衡存在、唯一的充分条件，给出了传统经济理论中供求均衡稳定性条件的对策论意义，证明了经济理论中的供求均衡稳定性条件；说明了经济学中蛛网模型的稳定供求均衡实际上就是对策理论中的纳什均衡，从而给出了传统经济理论中关于这一结论的新解释。

"Second Life is remarkably easy to work with, and is very popular,"

"第二次生命是显着容易的工作，并且很受欢迎，"

For example, we usually assume that materials are homogeneous and isotropic and free of internal defects or flaws.

为了得到适合有限元分析的模型，我们必须经过如图2所示的简化步骤。